概率论基础.svg

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") 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") 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") 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") 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To/eJOQfdOA0Ns4jIioq4QAIIeMWy+Fu4mPMqZzbLZCVEOqIRi5SKI3MyGSzLI+5k7vFV/OUOQlxWpeROEsVvUFPZV2Sp/OxS+xMy2whh1M5iBOlktuOUgshLD/d3SFkpb3I8SEkfYaSuRjC/+OS+KJahUBkt38VU5+/5/2KejJcNSUxkUKxJVIjXtbYpiYBNgz2FTNMv6bmIRQZ0tUeTW1cUBGYYqlVTswk5kkYGk1Ly9MQmnJ14TeyvkAv+lQTqVwuAkWVrJIAG7ODUWYQZ4uUCdxAdqOo5uLnMMbZDUGcsGEX064MNa/YHr+xR3xmBxSzoe594xjIhRWhFWeApjJmA0tTg/d18CsiJtXUPhAoEDRX3RqKVSkTLEaG8V5d9PRK1q2z8TAOVf7oRmUbUzINhz57QBI5LojzPR+KiRm0lHPEP4ExxFZb2TPCQx+q13kdMZrsS8Qbe9YMjmK4phYOe+pgCVepeqAwy4vAYmttzPAhUpg/Qbwq2gaq2BpD5VJiYuyw5sIyOJ2nsSxIMoyipNK+vMVSNdSnNVLmCqYCVMHttg3wdkabz5A/Jnsf2WPdAm1nQjoTil6sgzCtpYo08nlfJUscrBT0ITtlDUAb6HCUW8bu9YEieb9BMkyHXCvdl0DLGoDxUPtJ7wR8JjRRYRsaZCeIj+2wfr6XheOvET/25DZAUXgyJnK9B37LcJmNT+mSIK54IUvu5CAu+XAkhx9S7xaSTr6n50yG9i/Vas7Md+TzPBayswf7oVMRnZCFZ9aZ+LYI1L2rZXmWvfQhbSZjqSvcRP8T/z2vPQsG9f4oMZfI1nNjGSBpE/5RhgfbqjpljRFQnMRseANnS8igWS9+FzHN45g1kOVW9UXMIL9FtxQFoZmGGY6DsjxxMQDoib6N2R+rToWllTzOHFvvKZNcRCMMhhRTEiK/XDzpYlm4c/PpCa5122q9RWYi64xVODUlrI1Txt/UDjoW58IO0HPapS7C+BGNiyc177L4dY/CzrrUwDvsSuNedR4xpSGkgk4Rk5qwOKPiSWrXecmDyaeSuKMMhSzbKOwVZzAmclp9SHGiUAPcZSqmKYuYQaZDQiqpEsiY4zGxyHx7R/i2qGipRZ7Ys8uYMka0OakqU1FQdEU8HRjouQxX3IEez57EtI3WlHLWbBIi8/uv2x4ULatgjZ6fC30m3XwPR1HZX6xaFvT2viA8DCquOVWTvkioJulxqlzZQMdaTn5948Z1uw4Gy/hh+w8OHdu01cajB+u21ngmYAi2cWSkPCXih4iP5s5BKYEiNHfLcqlV7V8cFdhNoxhBIwccdGTedtNUSBf87nbqKFfon/ZYvyPKiH93eelctGfjT8e/UmvcBi/b5MDL2Ij+bz4Qpf2crS8RExu3l7yfMf5SQlSeKabW3JaA2b0xkQCNwVLQV6SCo6fa39IpU6DorX9vFwHgFLtwy3YxtFjUJkGDXrZkcHSkUuYtzDQmGobOhphV/CBHQXJDHJTD0nn6kWOv3qH4a+dkPwFpMU3vko37G9pxFB0ZSZDphfo8zPwt+pTcpC0d+LZ5TNIA7HsEx35DWZI/oAwbBlrHNW261Oi1T/8wMmEg91pxS8um39FBhVNwV6qjRiP+GU8VrrqLmBIghVWqE9LrcK2Cym7sGw3XDU1Y2+uPK5dIgCfpbECkiVKW9RQz82DCZ+vP48Dt6glFFbS3LvNsQevYCOhUQbkxl6GLzRE/Vyx1S3EbMWsZZmm9ZAbKRZ1eIh7oVZtYJs2TBNbcYlgcF6hGagpReXlkjHioAvC0NTYR4GypUWFXTHyqckhabHxvQNmqGsU0VJ3TaT/Dgw62JzwZtHKaeBKuEv1pmrExnxoEOJy6TQD1SLMCOtuuS7g9jTnNA2w9j0fejDmhPJISY9YD0rLCjWcCXBMBgZAshKynLJ/XRLD0A5EWHdCDkrGQybBK63V6rmByWtYHllSa/XUX8noANRFZbHmtcFV60cyamCRu0bpmUxAboAKg97s5OgR1F0PdxJyd6KCXi/Rkf3soQybIr3DUYTl5gwYUiopaPzgTezfMMDieTFi8awL6xhmHt7h5iNp7BaG6e9WyroSBQzMzJlp/DeBhn6ZFdBm2A5g0Ae0fYzxFXX0IUpkWPKcJ7bRkjI7+ycJjU/gQwO76lMHSw3tccatNYwFdrqqb/QCjxFLStQ79JS82TwBWX7VUHnSMs0ti1IHCiU/tk3SKjEI6vkhZ6sFQ8JIFoGlqCkhjbSmEF282wXtM4tS9xv+L8Gck/hdXbU9Q2/vot02BCjVg/te+wvLUYNyyR2goZMrVC28EhlIK+QZkg9UAdqdksp4GxzFPetRsCCiXoigEtDfqpdIVfOJ1TPQiGsWkzfMTimTFfSccqydJHOirwjDn9mLrNqYPKa/RJps8nPrhYlUZs8NQWCvKiXejdxJQNP9xwM/QJBdjeIhUbBIPDXyYI8mdKI+jHEMH3wHSDorGhlqzsw2WnxAnaVJNGRXzj30MgPWoisbKBreG1FI1kdYW8XNV9qOEnhKjQrwUXgSqFto9jr9q10yEHC0smejAn4yfrpACZBDeKMu0dNmedW7wR8l7JyDqNMu0SIvHXYFUiPjZNlFd1oyIjyXTMT0gqFA71crPUGVrg5nG7ACJ8B29ImDd4O9ZbJcAoAxDdh9Qte6G3nCINzrkDPFTXkx4ZjCPu9hg+Xls8NkeMCVei3oA18o5LwKmIJKN3AFZUs36x4w5JBh4uAuzZTidGJsRY62BctsQqqeDPbWBjF7vOMTjsvqxfSagBoQrMNb9wXeOm6+nhWiS7R4NHobMoxVKA5EbS/v2SQ0+nasc9YxKv5vF8k8TmbJtp+jYuKNvOGRmff1NiY0TW4mU+O470zO812My/FA2kuxoZkMcjGP5emM9Y22XjzXdxGdoQ9PQZnfXpylxFotEkhUxe0JUtiZsY9d1N1QxJxik9KTdXm7lpf2ZZ8N8i8PeZZ5ULOLtJ17KghWHsWhgfpTnuJnoNP3il/M/QyVFENpE97L4W9lFLGtQJaR6JnafcsQ+5TqIQIh+Rof6+h7D60wzyUcOETh2cNbQi5i6kTwSvRK44ZorMNsUg90gHyGQbDYe2QRZntIwWA5eDSaqB8lbY8C0UbjV+hhXTadD1oZCxFwZyK0MV+E8vTgyddyRslGHbYvlj4AvBYE3RLgRS6KnYaRiX9YWKcUuAT1Z5xwqFGvIvurbcubiEAbAqv7H5zYapFKxq1Q86+lD2JVB++shpo1RcJftt/VcXPCtj3vKy+i4OPKk170j9I2SCBJ/aLdj96f9VTzoBR0q3rOn2jHe3tHucwO32oqFWf4ruYfelhVeS3WK0qihM2+oFFkolr4nhyljHEpfdubbczmPmCRaqBoUvFJ50GCaro0eY14ECE3sC7+hapY77/VDK2UNZYPbMsOE1yAes/lYaHN/kValgh8nlLuCAoXkXLcxsyFYIceLI0qKqGykolxCHCa/bSi6GCFA9K1Q3or6jFtJnm6BVfimR6swaZA6wcYt4hn/Wsh0sWEZ0yB8iAkiX72SaqaWg/slVsd5eyJWwTi8xMts0yThoU0cZlMfM2xYFi3rxKhXv+xKIdUK3TE4ZhHdH7JVYJoFzESYG8IwNbSFYH16OE1ZmvSsF7Cd566cKvZbzvM7S183BHrMw4VhTzrEAzxDLClXi9I7jJAP2stx0qjRcucRNNMK2VseBKyr03jjtYpxDEkYIhoGVyjKZ/FOmDjLb2weIOa0m5LK9fDTsZOaUIvHjXmls0wHYX7adxrH8Ym6ovtDfu5Xi0enCAjOAGiBnJo/Gp0jXs07jpC9zm5bzd8NCALmF8sbGyU7flqhn1UbUHA8+Bw+Ey/TJ3lLHeWnRgf/BLrCni7Jb36eqgIDsy7SYJraFp2yHhIeSq1ULZGxLPQaXcYu3fEqfNub+DIDDKMHY07aUW/cj/kOY+8fxcnzpdw555wqLwcEKQvBAWoECIMrDrhm5sSxV6XEPKrn0E/rCuUqF5YVwXggyI+lBcNMSycrMvdR0Zhp8h2kZMP0LTxCDGouXMGjx/gMrXq7FQKRpAbBuFm8YD9d/tiyKlyXTvxOt7wPkDHWI+5UuYAlMgqpQGUwuXpDclDj1cAUxxkiVW5vBFi8XifTTNCFZbPhLTlewAZSIcRscmfgaAdEZ6M6C80soDK0UiAIKKfDXYXztSyHrKYS7EKW2EHaDxCBnZzkBPXS1ECMCaWuSDBbmtPbHswUS+lGTrlaXjYLGLQUzhqhMqq5GJmV8A6BFPRevJC6xqVknZmxcvU7+BiuZzc5FqBR+6AORN5nC1BqeDxDztGDHDBlE2l13V9QkqHygIq5CJUQgzfsoXlPwXPKai8TVepsBBS1ii4xrulyJBS5BNaUnKqUTDX5YL88XWpfnacfRdloGcABtWfqRhxkB2NiVllDBcfx5DbCW4nraofDVTPRjaZyPrKCMHVejXGSxIQMf/k65vmCAmJFesTbR4BlyWzgHvX5F5lYG5hlTx6GFn+7b5FPzuVIv5Y5Tr3pQbWQoZLoDh29FhA4jmjERcrDyIkzZ5hBIgCQeis+fkE8jAiWGeCVHVy2S5xpHxnQOIlD5qH/ccOqxVlJmPhjAJ9ORH7tiHfhOdLs0xlMW0W2XHoEfC7Utc2nCM3RG2OdI54RWQ3zZ8gCtlkyi800kNa8PWCMFNeANchQNoQfNp+YyLwLpKiDCz0RxElMUzrIZRCjnUtdjG/HIgfwD3RZSBKwlcNfKduMJDXV5IqaU3IZCG3wDcwt1A1/C2FOqCZiV0007Oy42WPL5Nnq/L/ITKpcvsU5B3Fn5FS5iW5RgVcUEs4G1GGoYbFluW/n9C4/dO2VspGiOaHao8TkIeSzVsKlmSjkEkCnWSnqjGkW8Dpm+aEMUMacIA9uUckJFR4E5jSvXnUGkEK/tLdRBwqFrtHiZzU2/RsV5ihMWNXGU+oGjaoLryaWpk8C/ZdNTTqzlD7gWtYyyHBy3xGWCvMzxKJawPShRlhkTA1JNeudrI9MwZ2lPHQF06cKGphoYQ8QWzOe0OS7VasIG2f0dEG9/sS6yqRkAuCVUqMQO7L0noIpueFqUgU9QCqlGKHRBRtgmPJvBvBNKulSAHofM1yuLZzWBMCS5/FVCwE9rMQsIQtHhnVnyshShyDEDeeYpevPxyWk7X5a57s8k1s87mcy7DYip1zKaGiF+BgMEXXL+df5c08jspBOZosSgC8qVgNrF7OuxT1aYlZYkoDeeDuFTJ9yU1ZuVJRmyLIoYwJ2ZnHH0RnTEYPwzYKoWHo7lRuEWSG+I0MSoGQGNvYVBZfSu56BMWsLi57OpLf1+7FETK8XzcBSYX+v+I3FQx9Gw/kiwTJgSkS/bgNyKRZzgMevo6vlzAaShEMDo12T6OIPUqHfAOwMajHrjYg7KqyZgSBigBXs524Pgk7JLqoZccn3rMGgBTPcsNflCaEG5AwzACrS0LSlXBoZiBilBsw9LV816hWAMrBMvaxpPC39OGj1+KLjDc/bu8aK6rX18BYvC9dPqgCgFu7Wnpuj5qIX3bz88tHX+T5Y4ILWLvw0mb401rh2JLByzhv5TG/buicEhRqQTV6Sxv+m1hr+GBoI7zxDnkSu/cMqcpAnNmW9D3phlk7KFy4g7vG9xNux+UHauJAx4EnP7RZSRSuIX4NvM9RsZqpgbWzKJpr4GNtkIAciiCaAurO97I5DRfGwnAyyyah2zJKDyGG/mIaKKNKlPwiiFEwwpHPD6E5niqS9TdxrKUdc75ngST7cqajtdfMsJ55QnpHGqk0j3p4WA8CCRqqxV4G5nJCKH3HGJ9yP8HPbN3Wkwnz7iPgOxikJDlNKy08ARvJVg6lBzIJ44RDzYhFQlgXnqiuFvHRqbE5TyDJariHWvMu43LAa99HTyleZkeNV63p2Y848kCHRyd9ZrJQxgF42TL0sDz0htZxqugKEHSUBLMwZ7/02sO1Sy+gmPqKiJbZabY4ch9/sA6p7YKhsA7yzKuLQ1Y4xkv83jDNVgIofx/gCzyhOQxzfkXxlMWmcbT1AIpdL5FI5caOlQEYyGfR/ffB4ysaM4kin6dZYl+SZUnqvOwlxdtDbRf4BHKTIux/JDcqTudBhLOEFzzzpI0Y6baST6fPKFkWFiVg2mX0osoljgHXvoZneFEh6NtZINVjDFvjuXGvPqXeZ+oOJhNxeQ3sTI0yC0E/M8xoPnlhWE1ADVo7dcDmRBRikk4VG27O0v5piXIW0WrR9LJPukcF9dHeK7cFEPqdDMKUowBRkLAGlp31kaMq/JCP1a6SD6aC4Xv4yIsTLc6GAH1b+LUqJrTqyrHECZIGpMAphMkaqOfNs28aIuVI0hVtIWS0lpxw7fsnfBS5HJ1fGJtl2/7wUd9byfb3MTj9L4655ZwGg3/s4JCY58+2IMZxOSvjV8H8jxsLn+aEsArxeV67TmEoY04fYfzkcIK9FW3OogFMVZnT5F95CjfR8luWi+GKd42MsrEcZzCW/qyqkrRLj19pCQpzft2vA8T6ThmfsTvAuOAvOfedx/bm9WvaQxlUcaZz8FerXKegYPDfIdHuLbiz8H6/clZzdmGcu/guNvQNCyE6Xh/3fgmoRnuATHnYkgybUXmzdlaISCmTqLZ3Rbotx13aCqvpY5xJmtS5QMvxADo6QS+wzU5l+tjlQwLfnWwEbWu1i2CciGFeM9JhqSWEXoGemcGORmW5RYIZlTcPc1FAsdNuZpJsSZQQCG3yrxdI+tRfgBi027I003YNLC6NaCeNhxOz+MxCEhKg0y1usM5/ONcwbjebZZjDHtraHsJ+MyWWB4LbupBZP5lTYoNPo9bnV8sPrA3bPL66X7s+GfNnxA2KemSl3ZXHpxS12FkhtvWZEpjdWrVWjWGi3M7vjedfp5ejJEZgF9kkGdSf4bBX9K//1liZYNEDoQ1fBgQFBGq8XgYghRRQEFB6Uo/mr4SXkuLZLYJnlTW9XTnw2nZkLbyfE6Z6NddTRqBDyOfkijuRyKjfOKHiJuV3JaoYPYVE9KrQgP6mJ4pdb9crEyYbaD7QTeQltgsR7iCayBf2r711wiu+rEW9uOIpuA9PjcIMMPJhuq4ORb3HqBPlVETD66EE4sSDoAVIjxOCvUdLO+1IkCGp6+vYGDa/HM8dQZYJ1EFyHIBTiESrrRneSfO3Xr9FTWbV4EDAR6pAzrNfKlAmjsQaQKLPfgRr7PFf2ZhsKkaowegLD8o9I6gLZHiQ1ONC9Gv6VCLbXxmNOSJKI57X4CrKgpR1nl8SRvmxNYy31aDNnuOF+yM8wZeAubWPOxBuO4yDE3f5qFa4A2AnyFbZ0iEdfA2QZR9tsXPIE5CTQV4qlxtiqbttWxJp7WJjW+rbDiNhCFVW91tsRRB5AdHh/sVDbHToqF1fhRG7xt5F5+3flW1tMrPbQBTnadsGBelubJ31AWHXH4M82G+Fl5GMPnyZBsXzzP3IekW1ftqn+QNRoTdugOB/sTwktnGzUMFOnWntSj61xwGV38nvo1FQ8Iu7m1oSGVc6T3h0jmV3YiUnLJHlgFAh3qkYERnVnq/BNUToJtyvbNqYcFjCU++wJQxSzdZcPlai8q42ZsRXNFOvQ2GgNSSRppAbZruXmAr2TSr7XMCbh+eC+QMimWQ60WFDQSXdLtdY7e5e/XCI1AEZh6/vBPipbFbgCW4eBZCorvTQW2QvMPm0QGxE78IDhgixC3tVaC5QQbAWa9BRHgLZ6sFxr1Ow/8OPFd8Oc/gLom4M8HSjNO4qWSNLx0ZHb1Q5mZnLfx0p/bt8EhluXeg7KurLe5/06EA3X99DJlEv1FeI5dFFovQUZd/PAR0fM1AJl1zxa3IurILC0YmAMnodTc8d0Fy3CQalFSbgIAIkIP2eII4bLOW1f62PNKjmVM7phKHos8AqEmKyHqxPaHxk7fu2JP/FtpjX4/d338PiKuGN4l9W8ADfd1L40IvS9OprAbYTg5Eay2//B3j1PLBDy+Peqd6TjIlv4jrPA1id46PRRPf6Cs91/8uyKCsUtBBYG9Il7A2BEMYyRL5QYsHfEUrBSo9Dyd1kECSMFUx4auwuOl/ByXaJPAEMx93Rri9RYf1QR86pXwH5/egxh09aspUDp6Vfr8qNiZSisHceHuracsWcvB8sHh8kYq1ifEIlcGuimd6ExZLJ1TX+zra4xTXwlC4qD8wB/KXk6VhPDv0Uexcr0TBBr+D13CSV7+ztAAAK6aiYHrpyPK0ZtNr4KP8dncotG3BkrdqfUBeOhexWQI7DLFrWSENkNy9Lh3YZPodx2cOOQFU+l87gmSZ5V82yLVS7F+C2PFvS/rb9K4ECJnO8WK5KTd2FWKsguzQ19aWK0xD2NrWKhk004S31lF134WIqyZINWyqhcyP7KzynZF87hjQ8lQCU51XOWViLzmMTYncXJAD0VJmjv5ay0yjFkmaSRBB5WCxBuKEw4aqQf5TqcJxzW/8tP4cePGSscp54yZMdlAksqQR6MrN3eLjhdLgWyIQAi5mg5Pj9NKitX6whKDrZAHwHGvN+YDsPJkjRfb8s5wxaWhaT6s3NLBYj9/+O9Y7zLPipBkNjjdbVT4YAjTyfhi3000oAjb+1D27bNvd+S9L7WXn9v/G0yKQys49Oju8qIY2JFFvNgLNnDn7Sbt5dzgbaGshDCuAZvuos+uqO+2vF2XkcJobwfYMCi+o53AdvmvnxLBjGaswCBv7Xkvwhi7HwYpnQZsy/R6xc5xMjgCJb7UmNwXUxt/oTfsInVquiNqfUEeN2Hnc4YqImWodqgt0uymPNIZJPrctkE4NTwvpw4MDMW5aFAS/p8hqOMD979Ofob7xO0zQqx7ep0VT46N8TXjc4AVEIu9ZYz65+mPl8xx5KHjTd/f0K1X8w+ezZLCDYPBoQ1QA5ihpJKOndQVdVqMxV0RicL4JsV3UZMlsK2BjGKQnM4TsF/GeFhCGKWbukAd5OoytREp2kb961qFB2n/lysUSDDqMuqHJ4uD+g8eNtn25LSRKfr8siiUaG4g29qa5FWBYqorNEuuyVggwsL0tvQjI0ODqU3NHGYziIRuiaDBuivUh5T0aoDgAv7DW8U2pSJNz+6qGW07W8GA2hCW6vcJoo71/lWHIb/CYdUk5hr3H67DUGxNGGUN4ed9XArj/os1Qz+jYAZwX3iZwIHKRQ+7GLrURy1oHn8ZvLeZqllaWxxrF2UppLCB+B5/3se9ZmyDQWvr0c84TrQea1Cfwrgk/UymsMaMv0GX7CLEE69JwlX+s7RraQy/Evh/vTD2i+kRpUVqGEZEYmpgswPs13SzSVwI0An/6F1KQ9VD0ttZhl3pIKQwe3TQbsA1xubDbRqjXcoCtG3042U2N+lsR9wg34fo7mKMiF+gMSc1e/fe0enm4o+etH8TtIFImWti2PIyZSnulT8AONwag8/dmrgk3IRGzmfC7CihFpVp0p1qnt+7KzT46I+ZffZRMh4ki1Zmtub0Zdv2VnN18kr9wQF5O8tQ4zJoCLRrLiFkOlxA7eMg1gdsf1vu5uUo/oX90n+u0r5rzPP0lHwm1srOGdy9LgP9vnxavT/Ggbs0Xe+a65GmcfYPdtTSiUWESPiHCwmSDEccS5dMO/foLAjF6hIhpAXHIdlDdDU6FmLFSnmQCxKqpJJYVlY/euKtFNJV55eRA8PM5dyJ36L3KzdmJjEIQnUq6VB78ZXtJiFXmCw88MR6PgDLmd1QUUllSPwQH09BWvY3Ae/kV0XGdz8MJi9A+w6PsHlvzjXadXb8+JrOrQvnv1Ng+04I7ojRpHzNz7SC/WQdZ6iiIosTI5OTyv7vbQI1ul07/s4l85oCVr8J5T4qVh0W6yHg+1FLP2f90fHl8RVJrqymxccYCFxOh06hSh5EkfSbOejblhypsG08JivtRG6TQofDqf0DyHQggVnJmVVxTtY6YMfRBc3uUyhmnzTrPzszqZj9IinzvQAx5tSVc5LyiZchFphQZjvMhVGep+RgR3CUBL+xtW8pWsf1JRmt4YoCvCcBKNQTGnem8axGgkBjVI9ra659lt+dkfTMdTY0FJUkrg4x2HxmtZb7K69+T529J+Cmmruh6XhdeWFxpFE/hAW6TbK4T2ZWVfCqxrmXuu3OKbGYUSNlK5jki0FH6I6fi5tFZj1qMQ186smQOD1n0eF96kxLdOd57YUwJ5J7+zPyyj2NJdZY9a0ePO3disY6nJdjsiZPqNg8loYQ3iKpdf/n2H2xFhu9cFP81v+82QcXOljTfUSKV4mt34Sl7ErHfU8Y5LceuuJw9INBNfFbm6qrJeruJwAQju4cVfXxl0H0dTHejqdQ9x1ZnBN7JZ0DqcWA5s2bu/7eoFtAhhau57v5PP2a3tNC9JV63BR6ed7DF0FgLuGZeDy9GzumsonE4o9n5eK8HXD1mLtxH4eVdkOoe6miaXg8eO6/1+3ADU/lk1ErwVrNjO5HVFRDyUPo6LaZe1R0WiuKh6RhccZqFBu8Zu3aMhrNe3QbXopB7J9wpOhrOPZrGx0iUwtEb2Z8NH/jDsEsnh07XfZ3K6zKF144mx2CQs7g7GEH72LVmaZvdXZ1QciwwrGN0X5Tpesju5NaIrybZoimQHSr/nvTOZbIS8KrKIqIZL5d+CNqMg3An8jmcIqEbCikJdvxbbDy5fCHJ0sBe76kw4X3BikdFQh3CO9Qgrqo0H003ilTIe2Hw7+TZbV1uCZ3FXOcRP8FNVpf1b63/tywJbV+sKU9YgWCXoL6aUEJFRQ3jbjga3UY3MUp6cYKVMYTJd+J5HC6JxPg+4FJZd49vIzXloVnEgiNau81mrBu98vLE9NSAgM92Ta6s3y1Uk2WbAxSDzury53mk8Ch6Dy9YeHY0qSywnAwZ+dip2cZtXkyuJLDevVaoXesEMkAeinN3tn3GTqQrev6jZDCfGIbu2D9Q9xgiIDV8p15cZIrmMaCNEdu5n3tacNYC2fS4BUHCpkhP3yVZTr57Cyxl1j4XkRdlMNmxBSh+TAx05CCVhokTpclqBeOkZyvVWzQheOH142ifLbcP/U/LI586dkHI/+rCMt+DV6d3Ggx/mzzrIYmbXEqVMFUot6gkJJsf0Mddj9m4S6X0b4Ty5sy9lhjwlkpDjTTNKr+svSWPjhiRhNA2gvObblD6Vxz/f9ZhxP7sdMFyF+C78FFghorFtuZH5/hL38+4JU0uhlDicBJ4/DZOofkpL3Q/jJvEW5wxkZxbenHFloqC1MwSFEix7K4ydkJkf/Xe43mR21zrfppEjMs+bE4bUQPpVwp5b4pvWUzEwumW8Ui3k53sTC2f89Hj1zepUs0bhIEZ3k2L0GzAmUMjSpAU9ypE3JYoZEK6a79V/SFvadepTSzzpcKcyB9dCX+mYVVf0X1DjKcGntbq/Z8ZHEnpAizw4YXaiBEHZ7iVh/1OQlS1OrImrSTRmelK5E8eW6l+Nk+MHMK26HK5MXHvLmtMOqvG5POzaa6Ol9iOMZcc9jP5UAy6zdwUaut3IEDaWQw//dSleHQip9MHaKRJfzNIuX21c46ljsvkkEj7EcxeqBL1wxsitX/G89erlYtNkPuOwv0kD6ixP8F7NAnSqcxn0wewIrBLylKKOyYoV9eX5BHaEcCR1GCZKuSfB7+f/UzoRhy/eSBHQ+pHsszjre/DGM02kLI/IeyzOap9ioMld4cJBBwcbDoBj2L0kl18itYdzYXfqkHJVCPxopTtt7wXsju1Gux5xC+2/qzHGAAHC2LVJ5eW92W26ePTZrMu6lik0FGokU12PcvhWeHpK/tmRRlSo7rqIk+lzapHMeTcXaRuNVUcGsGQG+UZm2IhStSd3gb8qWzYiek2tX5mjqx9lVTOXKY+fnsLsIz9bfrJXChG07+SzF14nN9kIlFcc+nsYouVLCwF6T1SXHGTq+CzbBjQkN8SACZ+oTwXvJYqfGeEAv1zHvd827z9JxnSQsdomdP6akoHR1eZWIrltXGjy5MsWwJn4tVN+ADbVvUA8qdRcvgA+KqbGaM8FGn9/KX5nJqMu9TCfF4kvVhQ7mB5+DCZ1yUL1h5kdxCfZ1kLQqrEoGvx+unj27sBCMK6p97QaHVJCcmv9THahbvASiSH+FIUr4Rnw2axUI8GklrYv9wvNhmjWdwvX7iJmYSsnE+zfs7xS9pOCjiGQ8i+O/PLHbCHkRRkASUAVYmC93ek94aFNmZl7evn5N5k89dld2axPbmUUxAug8hYd7EHT5qwUL9nDbKR3F7Vi2vZX44AK4qKYHS4fFQA5EKg5TIoMl491FVjc1KddyvD561tRz2NwW/pebSTRuL7eXpqXBBHuKzeGjjaXUdQ9GQgP9Jgv4/u0kqUAr0QqkSW9/bwGmRcMQovLrjKXX11piuJ8tSYIQLQKH00gkW56OJrhO7KNO9737qIXvX12pj/arEGje3ISxQmQ3IcR5FRK7kcKxhEEwd/qLo9s1QTrOyqVzVWwRX7q/j/eMsCws9rNnMKbjscJaqcaGAEL7qgJcjvvr9Vhz3obzeGSzO9fl6YxzRo5Hxif82fU8VaZD5zZtNvwvLPf22ZtB/0DIi+1qQ7MdJrpdHz9kGAwHH2k06zn2nK0TRew87iLFItJ1fGeESMeONhSJf2hAi48Gxcsl1+wK4o1CCW/oQnMWFBrP9qikiTq2SoYxSlRkWrCOUzDG6hIBHMZ0ODtyNvQTY2unz4XOQ4pdaTNprFCj4j+ARBITDm0GG8eXjS+nSLHoLbgKoulYcA92lIF5j0KojudGTjiOHYK/zire+oV0TKjD4Lt3BXrmgI2tw3QyVPNm7vTJQ/Zb6y9/W1mhHtieNVXOM4wcXE1ydEGa7UdfTAdiCYyo/E7Xmu3mXFYWXauGBQI6KQYkneBYa/5HoaU53nFdAwXu5d0Myb/hiG9uselmz189/2qR57qrKPhRsylRkfhjEwmVOrMA90QWQuiYHzY0fYjpCDvyRIPG8ofRVqYH6a6p8IN/+mdNtbvVNrhwLxhZ2/AhE1UNehxEaJVGHl8VWJHjogE4oVcO9IZ/3Uf/G5XVNuPrt5NdWVHDvubvKt1pldgg0V7i8t60+ni9xL/SeeFaa7ajhenOSf5fgw/LEHnt3Axr0b7kHMF67Pj7WDv7fpWHPq2EYxOLhOJ3Kgse++tAxYzplvs6USRf0zJJxhkkoevh6mXLXLleG91kzY77EJsvHP3gf+uUGLfTFpD/Sq0nuFMzC8fGPoEuuj6IDRcpOUx6HeRKqDrgoyJHTn/9M39807wSjVVDNNn2l73dn+nfuSKhMNFfwqniWsu5QmvRlo9bAt00GIbD/RnCI5Rwk1B5YD/C2pnBUv6V5c3TQKUYv6CqiOMW0NhJ/sKVuAXHVT2uCNyKUDORWivdwKVzDxoj2A1cTh8rLGr0pWw1XdQsAzP9o4vWjVuBbT4YKsTonLnR87nx1qbJmhK+F3o/XL1gQUqOi3MQHNAqsOL7AUZJT11lxMUHtugYZ/SaMLAqp84+KW3KRK82H/pRled8M0F98D7fnwRIdqICn12ozQ9PsNkSVZJfVhdSTtK6MKvJVVDSlcUbl7VYkx14QoUEwjFGYOp0SECi6jMQcQdGa9HZ9yctilBo1VJaqSMpSLxTCwkFA3C8Sa7j2pw2rk5uiocHBEJIu1McFDe2d8GfjBYKQbVnhMEv303CLGGXLMTzM7neN01XzjUK2Vjmh9d3z4vz8jgwzwBBeP7MroD1P53JwlkYuIl2tx4UWEJ0zJsdMwrYOuH1A/EIfOJn6OA1BrU69dgKrpm883cjw10M3a0Emm4cRggNhBqGDpFNucdRHfd5YLomvNpQGU04CDKc2PQIVOb+lnSCMglAIrg4XV2y/X/hhI45Hph2j63j6v6/EqXl/OR+nP6h5QoszApsvB6sw2629NtYOq6LXPvlsmMCmPpriK1DeR/21RzHdEQx/Hvi1t8g+JhQJTfxBDrm/c5ZBWwdndgoQKadgaHG7VDplbv3MR3z7jQfTKoym6wNap9XMlQzTlWFls2skdAlYSCu7qwsFbHlQcEDay0MGLyXPkyHos8H58jETLYPhDW1NBxufEN1Sy8U1IjnXc38MiCf6WD/isDynLm5QxDJDPkfU8fcUZNpYOj4BchhULGtbENTMxVx836cSIc6zjBZl4M+D3D5gOz1EcHJxWDQgtnNF0rRLKYWg/g0BPv1GVCGcXnUuZjTEdDY+zk0dybLZRbAAnTqH48Wa6vXV2tR89cUxS4xCT96l8E8ja2yOokKP9EuvvpXHfrurP3T582EJzdeNVTmdlza1zCVuHZ1gxFN1/ymQUf1ujsiXvel3JAkW1XqL7lwdQ3ImsLjTimLDtNGMERLXiilNU00lcCIWRN80f/roeIaGuR2eTOdJ1JVjgk1dqwiRLRqRwqE4COYxrVLqvpHrV0xJMKEB2mrWDCybj2kVLUXkPed3IoZxVQox9vTEchtaRgn27KgLL0gKhZRtUGkWGyS9DCcG4p+dd55/BFpyRyYetziPpmH9RhibonETx3Q4Cqx8drTjoKnSzOlkatfiQu5vABCDRtcZfHna+KpafQElJnb1OlhQs/QeUK7lidGo5tfbn08rG6DSB28mqlnmKetyHZWTHCLGUHVM+dNdo81NB1eFt3+Tx2GwsV4Znrn+rtx6peKRGzrC0aDjO9OVGcXR18zvhkV4ApYNK26wDaJWjBa4os8oSlvnZPH1LPKKlp8VqzNIqq5nsDPKGZ8ihFke81NTydF/WO0c4dL57IBm/R3n/08BOjKP1Tis7qzYlJIm/dBb9OWQuC2deratu+EzN2rtofq0Kz1Z5Olt2W4EVfkhjghCNJbejP6YILE9JF7dY4qffQuUj22ENwtBH1dOFUhpkjhzdkpeQWf3rou5Ec+fsrYk56oO3/WHLU3L0cTZzz95kyTWKfocsc5FOdsIWM5cY+mVDQaQ+yfJNUL2dpp05yUUkG5FjUIuCqW7CB9FQtCXGnugpnsLnTBIDQ7io3rsA/Pf4jpcCwRh0bAIkbnY0UsofJDarqEr2QKGegdpMezw5jB4cCYGqQpBFazAhrf86JDm0H4fLie0FawYGRW9mdHxTps55QyklvNVqxN7jWys48B25Yv7wl9AwuiweAb3raCvklJsXZdpPiW7qlY2vsZyhnaysgK2kw3bsQFYrHwvVAfgh9OnUosxkgbXcf8sIVRxVGMQXQd10F7kJ1Og+a803QzNpStQ4/n1HyI6RjdBMMUNmUxdPrbtUkpg67Z+fHOHq1PN4yxobsTBx2kr2TBSGraIwVZXkluL7eWHaGNfXBqwyGQ6KmtgoVZgtmqOMfscS6HTevJaF0/Fw8YjhaEAqdY3In6HoTd1nj31/t8Cfq8rHfIy/yVWfS6d79W4P5Pcfkv9SHyejc5ZQaFHpLKD81keQldZcTf2QO7FFbnFUx4ZKY+F2XMaZdzReOZ3Cn9RVQo0+KZcv4rhSN1WqAIanBghhSKiU2UqNwpIAR6+BobHOwyWn7RulxRgqLazLTmfXqsT382N6kkdcn/RzNbs1eFy6tsnEVF0O+/a+SK2pYIKoP9IcV2NnIUPqa1ve+0mVsO+Qi+18FXZLMmL1/2zLj/hQen1GpE30ZdFhEDFERk/n/aVHpRBBrMDaGTKF17dabm45EpZ6urXWJ091ITnqrrNZRbudTwyS8X5zwhHHTS5Xd5Jp2YNhLwH8AYgXwLzYDzuPboqXJVenVeCPF8HfJgINkqfwNh9y7lGgza2w8XXVpYNLILAsEBdGkRX/vOsG54DMwCFRPqGKaTEa7WqnX2fdZo0582dNnifA3TtvnOZMtrF+oUeJvuJsKCtZuYXohviDHgfJVpjB4/aSfl8V8fmSubw1WWTN0qFMwDbUzXtni2WIz6jlijw5K76Tp2j4Aa8gmyBFTWkiZa8sNjXRIdurKo8j6m41XF0uLnx8+X56Vuw/BVOE2HfjSox7GS11Q7LbIfJT40YDrGhwWOAroOhbYjD/6c6jWTlAnEDccu9D9c6yQp87yelhfbRTp0p6+0tpdOHx+Knhs9GzlCLFHVexerR3CBDl3pLr/J0KEX7/vdO1Edz0kDxiffJOemeIkREr0RrGMY7DGJPkyXwEbSi6bP24GYmPhbuEFP1zE+nOwZQm9n+exBYE7zJ+SLNL+liHiaSox/xk0uJ5k6hF2KQt4OMMmnNmHsX1iwWIzGWaPOCXl/7DIYarn8z78xq1iut9xnOmKZfB1jZ6ACxnTMOKLuNVR0R3cz8R4S0aHzPOZxuo7dpyIKv5zy0w+tZRY80hIhRiNRmLkRxvwBFgcwUFvZn0PHn6X37EvOQfNDIYEAhfhnAfrmEaAMY3IBQasnU2yAtvD2NDSfqUWPPeAGSE9b/CcisFioAMUpAPqPPSaSHZAF2JH2mP+kMsFUMCKa23e2GIWrUEGAw1WRvB5PeoFneIjOzG1XdWgwN31o2LPJrp7HI1Xouley9gfgB6x0WJdQy9fcRBbT25x4Uwt4jFWZxphapxDhiH7DwwJ9YPFrUQq72ZiTy07EDM7IbTQwAoaJgvogFlb1vnRDagXp25xaA5aILoubIhZ+sEOi3tzwzdeQGdVOEOIdx47/zb+B/p1DnlDjAh+Zlxs7vSGMJUpKzZnUbAknJfd8XkZ9dlSa/U547EkYiokJwMhyoJpCFVjWpfs7y8xuqG/NmZ8nCL5+0XtjKXa+BIPFkimFaVL+kQ/ablk486i4xzkYIp3vjo8n/bgehnBZs8BvCZheiKQELryv2485VKm5JdPFWkvkP5dkVBFFTCflbxuUJvbQBqUlShfn6gk/4rguj9O5ak85Y8rspGVyuVXzy5N+zZ272uR3f8p4DcuKTbWvXg9F2+J9P7G67kdaDcXZUbgCh7CKWhEslcAiMSxd+OwDpWC7GuqCxUqxRCkWxWFmm2yCV9P/6xUGayloaX2Jrlo0yxTmWVtOUuVrXRGB2QiP35ChWSmPfGiR0N+HpJODQg6ceSJlFI9es4Yq4TA30KatinogexBFYN7h2ROXAQKWxPRp+cJ5pQyIOKqOFS15yGHvNahU1nZZu9X5eeSvXoEhRvBf+WR7CS9Tj37qNPiFtMTzn8cEQ4nDiP59DV2hngyG1xNhF2l8FJA1ZNUSYNkLzW/xfNk6Aw0K+gGiaRlWwnbNxknLJlxcI8Na9+sqbGQoca/dzf6ZUORgd05GFo8vdmxLJlrKSY32BA14rg30rwtrHgnPy1X+KKXr1rUuE1to+iVxwxBsd2BTg7GzTHqox9PY2NTU3Kg0INhlDBZqGhoaLZpDGupDOmf6lM0pBG09nlA68yxGM3eoU8QLxYzGLYWcsc/7+phQouZVyVVQmOcT9FRoo7LIrvXbm3F7cElBvLkIegGdOzdSV4aPYbYE9tle4mqznOn9Q22vyfBYvQcC0tbHW/7e+g/iP5pkyGmBUl9ByO/nv0w0lutPsobgsuNg71U1T5eXDXJTIMGnZSkpyZPjkw6EJFg8NxasyJqR76luciI2fwVPsJgih6kgtxJiBDEUdTkdJZFzDoAeZoDNzTz63GRPKqz/nqe5VIMCtRpBFNtREKz/O/pOljwh1ODm7J7liYjJL20NQEpjEGdxufbnYEXaW1KjSqbye99anLpOUpbhbFxVGZUa+GBWWMr+iy1YrxwSqhn5c85Xi4O89OdeLwAq6F+x6DAizEwNJ563BkFwYyMqFx/AFtBZIbzt31Xrvkjhhb6nSnBNYqXdCC2SJ4AIniKgMIRG0CdkE7MeSh7O+v9Hl36ywyrbn9EOw/Dvj6gV7PbvVXXGtMzyyrmDU8wL7L165YKFSiVk7Ybtjo7ocmN287PKRJNuSFEAJSKdO73SPJXTHKiTlmyeOnQ0kYAWfmIxBTdLajvNZaNmVuiRgPEziKaN88hwGoxcvgIGd4jcssZAxkA5uQuz4RInxqN+FO0Y/AR8IrdLQYNEbIRVzZv+TYbErR+LhGb2T7JBUN2XOGH4qPELfZANmjQ8AkWOdTt9bu7PNmoujAlfI/3nNLuJ9j7sZ/WcmNlXdTZbuk5qqB1iZCtOnVQysrDHL7GGYM6OmdJuMltSmKyelZ/SscD5ltSg+nwy2lZsKaxLtxWY8GaGRC7lehqa8hicvKW17zkhY2JGXllBceeuCFuc9tjH2x02MvsiN1pvvNbeEWZE2z7T3yM/e4nnBXhwUyMr8UhYnFs8+JzvrvFCHelw3eArKOEHjU3v0H9eijpCdc06tPwMfprAbwF3mjP5yS0IirclOhMFaPNy4gzBPwhVrrVAADLawJM7dP+1ANxC5+2c/Y9OterZLTFdw05KLbpjCgo23UktSmJr6BATXQrpzzqKm7izsGyZJ/lY/PQs9Q7BNFOlcyAcgnXDyfve/cOPFK9DvP8gMRvhNOSldfm6xyWwGAjp27xGKx0ueFttkoidav/BD9Ota0uRly/NXfbRgb9eAox+W7Nx0cdFtKOwk1U3lV+wNdM6jePJbVn0l8JYlnRDX7CwWpbjLvG/GtmmVf2l0r5aMlbGRy4SgXnVGqImvdaamBDfbWB7cVqQDrvfgr/MFTeLQsY/h0SZ98Xdom6EKq+W0OM7wTW+neigNtpD8F4DqvsbRpehUAz0ZXhamJpR89nxz2pmULC27P+ntcYEo/b50AcRBF3PEAjg2NbowNjx0eNjgejWWFggOKezRoyfRY/60mHF15cWIgfyv1cY3fA7KX5M0kJVaojShD3/NcP1/sCS2QcH3uBSdqUiVOPmkluZ7vVjtfObG5d3JeZ8eMOkfiH+x+JTphexyhBGRu1FUqfGVnF5C0i0LTs3WZDQHaI5qQMhku6Gp9bQzSAuV8euxakwiAbJM9UJ9yj2HGjXjumrUkWpqN0F+Gzf6iMZxKl6wkuqM1EeGU5emlkJDO65GDcCcXg2nSLpM1oDN8Lj3wNwid924u7dKtR7Z/JieskND3Mgc/BnheqnQY/26I2Sdr5fdwac9mwHk25EWImzEzJffOlg2Vwue6rz8gc43chy/M3MFMHqD9TR1drT65jwnMCBR0PQF1808KwAE19A9NLSGNpO5rrT2uqYGKNSOhWt2XcBjvpvzLxV4g9iOYNrP4jX8dIvgtD78IV9qAfiBfh+AtbS6GltcxKUH3tjkNF5E1cyGl6uVsgHhO5lbRUML5O/rMQzj7AOyBWrX2Y0tP1Ly0divB8bwjpmpdFpWpjg+fkBuNxdJaBYIfOmyytCq9Y2By1rMK6Kakj0381TFa4NrZJXTB+UcxvOoK+QJPQtPZy/T96WUtJw57+xVAg758IWX+HBDTRk1cBN+FMgI9BNBHX06/Hqp4/9cZwMvfEsSvZUda27trKsstvvs/9oKkXCWK5tHDo8vElELgqbRklmSegIw5Zz1XyWuBoZCA5EvtucNV/NsTEQehylX7gkMZ0Sbdr/K42zjeUKE7yLnny/IC547zkCguCVju4rJDWVYs9dtIaQursdK2EAc/6zN0RUHF4sCtl7dt/glhDvykyEvPJK4p4keENBXMiZxuQm1G5UJTeeKUpuqB1o/7IPbOtCf/f99s+7rE/iZIViuhQ9/CZhnLaexuj4IPsOWjMwVYhd5jnseau/28tmBvbseQUycTWspMHYaSb18NBBcIHFuAJK4pl/+GYzWYKjwgCisGHQchbEYTHFpXB5+UMO648PECqfzIGueMzWxASxbih2Ni7i9rODOTejCrkCXtIZvfOZVhoh1+CbdDM4dp041UB227jxvjblotB5OZdCOZ0cdgY9dJZiFqwKw78Hpj8LZvT689xGf4r7+VfsUEiA9XBgiIlaNCinbUVVTO8qsyP1cLYk2LQ52TYTFWYtl1qYTjbHyfLMKOY79LW7ubVsyV0F1/CvRRre5GUdqBSyLoU5y/mDaZPG/VHY0kX9z1kBNmHFGFUsnhf6aM4+7v7NF5uWv+kl+eY+3/F9XTws06nAI4zZxhR2HQsUN2LPWXx/XlqxYKEOukSjbyrCNizioxALSREVa7Z4euKyf4Sr4LhzYqksJHjvoTMzwgh5KsUTOizC8IlFckmQSozqZ8it8szoI0QmDfolqallSDaSCZrbhGXCx6Kopsmi4n8VmhClCLXwZtTF5jbCRZNzNu3N3i9LyWpl6LGcmrywRu/HSaVTjpztpnEwbhnFrFnvCamLCGdU7h8xJRhDiopVXS2BkkuKkRDtY1FquAS8fsASs6xutoKbA9kmE6QoelQK5rTQHT219PO8PIbX+d+joSXRIleMPF4pfvbGuSkMGTLuCX6qYPZJellRJPupl4GqxS3ZoqViwqXq9mRhjarbl41ZyTMxREHjEvhSFowQjtEsE8y6KERD6drfpj1TIegclYCCAh4l4JleVpwPpeMoQqul1zDaU4B/IV6OENroB48gQ/eBGTSMTqMZaVjah7Dy6Scfc6DsaJ8XvCjSMJBJPRNfHHsSsR4UnmJx9akDzFBjhPwtwFqkfPqbKGOJrY8eM9NVMqL61h634baATIx5YGVkspDtO2AUCwraj1MQ9nrZ5xeC49AZKMbVp6o6Bxat3ORALnbgyOTv7ovxkOM0iznqLgVx2SoSJ76hyOpO1Uy1YMq7cYU7oNf//72DxgtJXw1SIVTy8G9VQ17oQABhCzl1UpGUyKrrdgb9EMalnEF13UQWHIRExHejQjYSCJnWVKD6G8i2sCgaHSFhK1yNe6jOGRwvq+C8DqKLYDy3tcdN4tWwFSYROk3AQod6Qy1VzbfbZe23m2MzczUisLVpZP5xJoS7V8yBEYgt4NRJ1H1CW32TXTSED9lF9U1CW128tI7T3L3KZ7Xm/wO+DOw+Ltxkaw+eC4vokO68l8Pxds7wUE9cnZ1UKffow8nzNL8D1rPIQg77ztaW/NBZg+1cu5OwdWQuSweyn7s1QEcvN1dpVNGY0rF4HG292YT2L0MTFw/o7Shl0lRGFc/T3stF/V8OrnFjDmJEl8XlVWTuT4bp0/Svs2PYzuq5QEOMCIPliCpgGfCwOnjpsn/+WTJKg2gJ5nPGMDrq8Xx3/9srbjneaC7eDjLfQYzol70O5n1l2ldrUEyCpOzPrIjLW4YaEcZ20+RmmcRUiIpRxWdqdNTgg7FzGA0SjI7++++SpVCdBjcUsBxRLFD5DdrgrDV10JJl//4zuoSCEOwNDFW+FoIYH8vLKyy0Q0DOlDebJm9ndHx2KYgEQ9d8laa872D2guBG083FjQJKDiB7OapBdeOJ4cU1DU8DWbLkn3+WLoPrwp6EGAgPTrvQY2fBCutiwypIP40OJ7P/rgwk7Y/CsQ1IWs73kvYp6Pc5acgGcgN99BCw3VtWV2hLVo75Pbntnki1b+U4KZAlA5O2zm9LlgrI8XNdKParKRmk/RBgYIlrh72pKyE4VT9Ix4Vqb9xQY76K+1DyEJheM7TaZc1zHT815OSqq7xqIc4pzE1ftSB/bSI4/htbwPF7UpdOzUkFfWF4Q+2EbIKn8XW3e3SwYG0Dg7dr1J867vFz6kx0+Lo0vIqjt+pMzxxraoRTwQbug9oNGpUjh4YJ2DVJ2ePLM1d/s9LP8q+sl24eii0rtXJxJpKjcmg21K6lKuwCWetQe0i8r9G8bmw71csf+O44SFTFWxHsMDAYzvie/heFG7icxD1FUUPbZTWQEKFwPYxZZDVD24ui9iRyuA0w+t/XcAbo45dyeJalS7whVkqwPn8JcAFzKXeiK7POprGFjBrSmb91t+Oft2g4DQ87P7Y0qYAjwGiwcrdy2avpL3sBxk5xlsYD/Rn96+bTi6MHNwfVW3DLN1rQwd/wy91T3xkDMKgbal+Eq7OAc6klxEIJ1nuXLOsAUX97CrkEh2EOsiRYoZcvILXxiyBbDo0lqvIlJtnXLMiEE3fhuxLh0Zy0FUmJvioRi5bDwfYYX7ysWIWvyrs4JyZ62Kz6aM2afLk3h+X59IICyudkBGlDsKoQ34KFPsVbBJestqBfWRLBmhiw5ru/UEs1ySXeutC+4F5wWzVe3Ra8+eLyt2nSRI6QmLriuphOE7We3tvLywPTLM4/1NQP8Iy9M8JfdmAHdg5jOVXRfdG9+qiejS3XoCweQdKQAyqnwKmG926GIBwarhmwgIt/UQtI1qQfsrJiFjA4Sm8Br2a0MVXoM54s8XndNYmZYfsrayRBiiJRg9tuT7Ny1GK5ySrC7VFUgak3T3UwOPy36EXKIMeli81evoWtz4pLNAgnEy5lZR3H6+HoPIoYCTCvlk3sWBe+XrD/GrgxYcxFoTOGNTcjdBFwvz1pTvqsApyGXcR37D27GI2YvGerJhB1y5sZJj8BTcrfUxiPomPTz6TGnvdbx0IKpM4xiSX615nIyuNkfH43d7BLyGUgi4YKQuKi1++ck7EhWis/JyyFaxhcoX4kLLoFhguDQewumu1rG+35Wjh11Ves0VzoFSR49S/0x2tw98f07Vt62NCzBEntAy7rQiPoAKvdZHMV4SjiwuceSh6eg7lFhL2lNou/pwM0XWBzH1S395bxRmcTk52ggBEv4S6Ry+kkyzfMq2VUNVQ/4LIvNHWA1f//x93pSBT6Etp0QjaxjaO5JnumjeACKHwsm8h8KHmYCcw3V3m2EUW8XB1w1TSaI4BxSqk1a6JfsU4c/CY8UfBxfvWC70M4C3FqBtQFvx/HIThzUPuZnbsKUK5LtoGYO8n3eUn0CI8v4GMGZW9hUYirCyI6bmeDXTtPCiwO5VWr/POZwazA2Ve+3q48/5Iir6+r0+fztOibE2NLrHH5Xhfq1yMyZ+DNZ3g9BQlqBbYRRR/d/+kHE5+p+mCPRUfHUZrF6IgHBMLIPtwPXT3w6Zth7cD8RUntSEF9Ye39qa1RWa2uVCwsgtaNk+MF3LSadUx6StGdU0uDhARiXEO6rMbIaBsAkKs1MDZHxWOkd4c5s+1tqcLuAD+1ivFreqr/8g0eW/9VShXId8wvsqRNzptUkX6z2VHjU7wZofx6bc5UT15+3/f7Qyd7dq6R5E9uW3LrrO78ZpuZv8dU/PBVf27lpSxrTq1tUnLN1SJRgn5N46sls/D0MbCB4j5w/M6Fhc3m0QKczryEoQkgM39kiyWbm8AE7AvgC8hSgAV3cnFWKXWJKuVgAWAAMzvvfcwo4TAd6/oHiYTR8avwEkjLa2Bik8GQakiLEiTaF2ZOKfqwBwqxpy+r+Tai5HC3OawPJQn07sEdUgGT3crnzKvHnQJnMt8poEgga78WagAL0yBo0XclMwxZBfNT4f1J9KsXO7ispZkQlbn17r3m8JS5zmzBFNrlCyAvwF7OvCLuWXpn3sJJxJpc9Aq4sJTFXnoNXJVybYs8gcpXbwcwdYnOaM8KyBLYBy9WXHz4+bp7+BHOQrxLvENQEbQgi2dhxrRdCaF43r+SHJzHXyv+W/8rUSI6GB9xFnzUwVOSxu6EPOvtYCy46E6OrWL2+ohYm/HlSJycw1OyUUZ2bvX+cTZ1fM2UP77GLHaMZKfKEcYZBCYzP9iWVZMt0W+N8mg9I8lc3wajd0dFbYazwRnZ15aoXK178eJZjoGPrvEUFmu5xUSxVI8rHAnPQn6W00x5WZqQ7ERWYY0d67dbeq3M/OlMriuR3btwHf/FwO9czsPZE+Ajj5K3b1EVd2L2Q86Py0Tg3N/nhSaneeP2Bylzf8qMDfvqwowqKr6Jpw7WCGaduGTFYTMBH6VFi/FZnndGvNcfhN8GWD2MH4MVeMbbk7MtHBucHp4ZsN479U9/zTB+TCq+sQhf5+I0fghDaGqiAS9xTZG7ROkZDnVoL7RfMHjV7BCmZGUKmx+Fx0zsEH66v2YRfkMsPTZKTKveq5/gp+zT5m54VxAH5rMWaOT+PvDi/RPhuWZz37Dtsdf3+xDmYfyHb98/2wkNnSRQX0w5QtRxWKd6o9GMJ+xHdnop8+1R0IQuZWBhIyEj4Kfva4n/bQCfs30zMicCP4PR5y8QrIWWUWqeOkwdZdUrkM94WEAFJLAMmOhYRM8wlYBEV0/gigQNHU2g8LXDWYuyajGKwgKQNWye8waAAAQAhM/WBrnsULv3B/+kHYjgej1DcGAN/2wMZ4PnMDiFSwS4i79gbeqA/h4SYVgrWmuIsAEP+ovY39AxS76EQwoZeQ/dZf8JLxf7GrzTU0PbGsEOLnaGxd5b9BathiupV0bhQRcukDRWYr18eoqivZsvImkFq8lZHf6GZ2I3agcs72U3hbobES/ZVF+irWAfgEGVl2pv4+QzgmSMrTlVrbxPEvSLwbbOYTdsqapjrp9LlpO4NEcFm3Rt3sC3JYH6PK3u6i2hJBW6xQ3r6U6xrZfbU6hE5js0dVo2YXgoeWgABY2p10EQBDu1qUZqPad4RQtw5KS2fldyV5+I5/Jg0is288+dvgLKzcMCCTSrb+cr0atQ8tVyeSmULwimtKaeyH0oeZj4IuFoKJBnHQUk8yr/xWSoSMkEyCiVTeTV9Ef11+TdhZ/I+CKRe5H9qIhQrI7Xvp2zLQQENdXS1oUnxVrIr4PcE6mfcLl7JQu9Htoh60gS7AcArP2+oXpoWV11ZcMCUQi7cfbqKcH/xvtcaldY1SJWMZqC8nq183H6vGM5ITULGF4si8FqXrG8hnMDQnDcbMYJDK6FUxiYiiHQjR2JTicZqZrJ9cX9V3lwXRk5NMqqw7L1WDbGahlfXs+pkgVV1XPGhYzAzwXupLbgOj8O3n+/sqqqUrneMFxZSWiaEjtd3jOOikr7XCRUDmBXHs3Tjnx7/Ly5GZbp6po71+kU/6irqZGNnSX67FjalPLu7k+vKtefZM88uH+mRh9y11UGKY4oUaJmsclzbhTYCjLymjKG3+ssyeSeTN8dLEXYfDK72J71LSUvWwUdpSGLlapDqnhPO6hwa5G12zjb25PefSB78C5wOj1JnDNvsvWYgBlKeuF8LaLrW4k6cDNU0juvRK+i6mhOUx998xPsuhjUQRC02an9/F3g1x/m1xpu3aIiIqg+j6F2vvWbbzRms2A2Lz06Z2vLKyvL6XzA6LuXjdVyQwqHfADRaHtTQz6C3gulQ0wO/anBNr/XUBxTdgxdWw2cmeIHuxNUr0WR0jf6GCUxFIA4TAgk4PFjcNF5ePIn+PAcDuzDd1Vc6H0fnG2/Ph2DAQH53LfdPogAMHZ9+pay+/c+7t5Tiftgzpwrv7DfrG+c9Aoag/DJn4DREG1OR7whfsQVoHuXvEI/L/jgLHym90aHxcAbt1JPtLUZ9kj2GKqqjrnBApyfZoGjoqjyFJd9StnRvi4cvPvHidQLTgkcu8KUtW3gzydBnkuC/W2gePsGjFuCLn8nH90GcmZgV1Dm5iiry7SgZjddP0DrzWialFG5mYlewZjHFp7jcBeeOwZM9dgmJmfrpPwbJazrJZPy39tOkHQoZWltfWBZcKTFKl0eXB+oXZoCgaezm4MhdmdflsYam+PRMNkEm6MEipI0vDsErIjgyCFm33wazVPY+1uNQMXk9halkr0h4OnfgAuDXK0kWkZnYzSYP1ie3stlqgRFMTHFc5X0+gjQDTNmSaJwL8a55Rk1GAJDMIsGwTSYmauJcWucjj5gfF/AnfjuFZumCW/aSAqpOsM7gbf9HshdC2XXQkD6qKBncHlaA8HA4ted7/WD0857WtwjkXqP+ei7CS76duB0QBnPize8YX3LP8t8ibsWyq6Fs2vBl0x/KgxdmnqxN36BaIFtxQOb34yOeNvf/jcQtJ60CtP8p2ZG7rmOLxcG5YizNT17t3cG/ZwUfXIyb31NvNtaxZvFCs8TOVXNqzcMrt937cl6cjAybrQvZM/bgpm2yOSj4uq5G0o1zpA80a+7iZYFnkreEAVuXm609DsSMrXVYhotHssR5VjpzL0Gm2Evi24R5eRg8TT5IquNhQu5QSVwqzqbYw+0u62+HMO8Kf0s9j7DPF9Okac4xora6eDW5WR/2iAZFpFn/kHPScpxm5ejMMzsah/od2Uai9Nqagto7ANpxUZXZn/7ALMLhtE8fev5u9IGcrcn0pHf1b6WMY6oBU/bGWvzPWsyy8venWvaP33EzGePxg5acr7ySpl6Gui+SLuA0mubE+fAPXcOb/+W/Pbk/v7fkmRJUx/v3nzmyiLBoovUgqVVZ/4bvGXNyt4v1IL2q2tX4fj6R22Qnm5yxsaZPtfyC0MJZ2r9bZHYQBBGHLjL1oCZpFUmeTdv8gUvHnXXF0HWy/QyTnaHY81egBsJIkE+e76+0pJQluMxG/W26CyGzX4pgJwn7KmmhQNJRod1B10iw4Qbriz/k8sNgP6ZkOnooUqT9OWgizl/l9utLd0EsiuRQDRB7no5I6gxskGLQAu/+ZtHd16GrxYEtR1zAmjfXmhKOJwG7BVwnV9JvvjB4Ujc9UmNARgthaFbR5XQro8tVjwhA7L6fpjOUAXZaoY+Lu8AGQ2NvVFYXs2cmkDDFT4OW8X5NRASThOHQDnUPsi7FOxQeqZg3R8lT0ofMwwksyT8rVusJj08rFaBQCTBiJw++Bljl7AIQ+M0dc9yXetHj5a2Wr5Au8pH083zB+avta+ZhhGMhHY9MtJR3X8fY3oK4/QWT8J7wsDIfO1tC3Zz/Th4KHk4dx3Bi3GVi82vAEiuknvzgd3cyrECCnRhp6qJw7+6usnxMQob/NhTngqPJGLvBZjX8194jwIy9F0BgKBJIP0FnztxD0+9PfcmAHHYd714D0f1F0Pi6U8qmQyf9KId2n+x+b3gqOS2e70411ehnD6BMHoUlsrg0WihREjyyEK8sAAvXNBRiW6uFopFwnuJAG6tlBYBAdfMK7NMKFeoFfKrvxD0cVCM6efgfmDzA5zjZ4JT+WIBuz80TrmgX8Qe1AaSoFhjZVT5I4kX7uiIh/5tKX3AXZnMawztZwvE+yjn1/IfLflQSNUuYtFDkIWGeAZFYKaLQScqwKAbYQHNKEBS0VtOvf4x9TV86O5GeA18FZhfc6Ae/hHy0LObT4nwuSIIjTs/W4EBoPx+ayxv+v1sdP9iKxDkddvkzcPbF7uzGsVXjd5NbpwtxaHvBjPSYAamDnIJtUSIyflqLPlZdXWIAu33vUg0Xih5K2pVG3jLsq3IBpV8fgFv+X0SnHRCWejKl+NWNP3ToTIA9JlNRZ5uXUEXTB+eJXn19vCr4Y1DKJ+vU7Di91Es7UT8tU1a0YlsUa+Y6PUjtgu66dAGflbVlshaLPIYiO+ph/wtHE5bBRF/2cPOtcNujm3Pw8YYGY//YgmnUuPG2to9YigYKBhpJjCmIVXlSawh+x07WewWK5K2gcb6rZIjMOWrYXjzbAh7TATlypZc8L838qRzC1bQTkhF7Bq4ZxWJESumvYKl20tcBL4HpbCQT0Uz3Xa49DDCWEUoyl5zUpn++Z4cEuTh29WOAIHH88fk6dAkCFFYcsyS7JiepwPK3AtRenHH8UWyhr2ac7n0E75/vUWFNa7o20xFDavgPHH97wS3/O3IJ2t/X8tvTYaBz5VY60eEmIIMoTHQIWHmJhG4RhliSezhhlRocdNJO+TIcyCrmUY17xOWmuceXewlqj/uUQ0UyM/VFpgv1xnHJhBI8eht4v7IEPqxVZQWKKx1hnnq4M8H6XwmkA6B6yeu7hsr+ZP+MQN5RI/f2h7/B978t/XvM1lDhgGAgYFgGcrIICjtsyfyXp+k3rbNMmjOnyBe50PLdst/TmlWXrygKlZeX2KuLywQ5TMXqnDUDNRyLk2qyrUejkNpBNBCJ8fLUT2DnWwuiQYLxi4sUIgBYMeXzG4K+ZQiPxacN/ep/y0oD5DmMtJC+FtKo9lhwiFlxeTuTdYIwXHxA4JAuuvJGOa8KcyvuAaqogFSUDF42VnLEyLT+CpCFtEukAFV1cQFcc7IqobgiCcTNCSkUkD7PuO7LyUjsIvVqQ9ShBhFxJQx4stj1FyIPMtSk8qb+yY4NuAppY41RKYDSAWS1yEBiuNyZrwyN8nIV6UBPFueM6sMU4S4r4gmQd6kcTyYh/k7Z8hCuPlSkXsAi14WtAVoeUlTfj4Nlh8+IF3c6prC/RZFbhIllXmTCcDqSUBjxLkA8lEiUbBvLxViv/xZPctSBvIgSMfMNlytPk+ZIgf+bcHB9HlTttyBkbMkdqZNzyiPSoMSfu2ktc0sxJI90ZGqQbf36UkaLMjV8w+UqA6SMQA8JYqUKKRcl5v4HZSf5pdRNbJFN5e+nMW4mDPJGV1Q08u8F7GjdBVfKiKcOMvK+rWTSgpVnoSyz0IALJ+TLSxtD7EZNUgGesPC4rW8dJb8DlIWkDmQvk0PDBbGOUdcUAR+6cpiMxLKbvYL1FCZLw0CxxKWumfBn30FdCvIHRBb8ka4N1skGzT77E72xr19NnA8+VRwOraGf99A+4AWHETH31MVEssagXyUAzYJph7zfXnFlHcStztEYOfuMJ63dkc4/O5OExaYTF87pifq252bdeFdXJ6EcpKdzfGEUskUnECr1pk34+mneLLYJTUot4IDxsKoxXIhEjKm0kwvTzzbXLRrLNQtDRLkJJqT5oAoW02AVML0pLCXa+7cNVGiqqT1cGfZHaOBSrPPnAOlMY7RuY4rTXFZo/u4Gnf+Nm0Dp4mX2gkjM8OsqAYTvcRgciZIOblixoARn2T6tuFaOxCmQvPVj66T/jkJixQ9E5neGtALRh1JzRisIq5y4oJsnIlF7+caRMjRPgV5gJldcigc+LRQJejNYmjhKhP+kAuIJTdpm+eSYDqjoVOBI2IucOE40swpCiufE9YRtbcnWr7MmGnLQLcnrLJTOoJq9/xxqVBxhn47MXg1mRVTc4q0/FiZURR1JI2b4r2kjFGHkeTXxMoyhryX/0a+tGK4P2fT0uufIl4ELTTtmKjf8c/BMLGwcXDx8OEIJIqAkIiYhJRMkGAh5EIpKKmohdEIF0ErUpRoMWLpxBXa/854RgkSmZglSZYi1SRp0mWwiIlLSknLyMrJKygqKauoqqlraGpp6+jq6RsYGhmbmIKAwUKLLLfbfKuMuG3MMzBuse3escMXjjoWCPjSvcAQHULBN751y1fezttkw7Rsx/V8fpzJYnO4PH7HW2i5lRZb6qdttZtUIFSwJlIUKymrqKqpa2hqaevo6ukbGBoZS6QmptZlZq2XYmFpw2a/2LItJi4hWUlmP+eUkZWTV1CsIFdZRbUKn7pGLM6vpa2jq6dvYGhkbGIKiCQIRsgUKo3OYLLYHC6K4e7ce/DoybMXr968+/BpniHzLbDQIsNGLDZqiaWWWW6FMeNWWmW1DY87S72FACginqIcYmUuZsA04eIH7OPdVDCHpSKYIoK5rjpXVRcbqnx7VcthqmFb81VFdXJTj9bxXNSapQPAMEBAwYP4tAapuv6a+k6E/uYIBZ3f0eUVyPcDVjFlPDLG2Er9gRsXwcCOsgqU2g/1Lerlc8+dszaym15UhhpfVIYqZzSrjwmQhRy6Akww7iI0cckjzNJ8iQLAoDaIPdFgll7ryDG9ubDXbgCt3Q6tFcbAkrNRycz6fw/SztVdr9QsOcMwX5F/DVTrhVluFjK5UnckVSlpP1mSYQDp0gdGqsCSmr10rqiEW2nHU1Pl7CJYspEbaQ1DKFdNovImRKtrmZ3e+LsCnKom2xZJzma5RksVEw6AiM8/UyB593JVL7XMEYH751MZiTDU0DzFDJ0vsgPTf+sgvdWhg+wzG3/Op3n0K5vQKjawDcIRCDgc11/rQK1YOvcL9J/4DVjm6Zoxw10EAe86fvXdOzMn4pgaB7L5uxCWAjexN+9YYzGDgUPwFEScRQLDYkkG58uUb/XuReYAykCfKhqPXvVsOh2zNGzWxXMbOGzeogUUJhg4BKui4IZQr+cdqVuCpkHOC7iw4Y9B0PL9o1DdZzedHQOM+l4LYFHn1Y9BGJ8Gs8aVGlSYVzHrdwagATC2ygPsSmARffEVIIDjNgwaWS8+ahkpHmfVWdrudzAwpAeH94NyxHjRGWwQVJVEtf6rtHn6VAhG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") 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") 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") 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") 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") 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class="zx-node-hover" stroke="#5EC8F8" d="M -4 25 L -4 0 C -4 0 -4 -4 0 -4 L 220 -4 C 220 -4 224 -4 224 0 L 224 50 C 224 50 224 54 220 54 L 0 54 C 0 54 -4 54 -4 50 L -4 25 Z" fill="none"/><foreignObject width="180" height="22" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(255, 245, 197); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 18px;" transform="matrix(1,0,0,1,20,14)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>条件概率与统计独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,229,25)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path style="pointer-events: none;" d="M -7 0 L 7 0 Z"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;">99</text></g></g><g data-node-id="cr9ep5tico00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,398,5598.2)"><g fill="#E05D4A" stroke="#E05D4A" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 25 L 0 0 L 256 0 L 256 50 L 0 50 L 0 25 Z"/><path d="M 0 25 L 0 0 L 256 0 L 256 50 L 0 50 L 0 25 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 25 L -4 0 C -4 0 -4 -4 0 -4 L 256 -4 C 256 -4 260 -4 260 0 L 260 50 C 260 50 260 54 256 54 L 0 54 C 0 54 -4 54 -4 50 L -4 25 Z" fill="none"/><foreignObject width="216" height="22" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(255, 245, 197); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 18px;" transform="matrix(1,0,0,1,20,14)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机变量、分布及其独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" 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-4 54 -4 50 L -4 25 Z" fill="none"/><foreignObject width="162" height="22" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(255, 245, 197); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 18px;" transform="matrix(1,0,0,1,20,14)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>数字特征与特征函数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,25)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path style="pointer-events: none;" d="M -7 0 L 7 0 Z"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;">...</text></g></g><g data-node-id="cr9epcs2ja80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-182,3137.9)"><g fill="#E05D4A" stroke="#E05D4A" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 25 L 0 0 L 112 0 L 112 50 L 0 50 L 0 25 Z"/><path d="M 0 25 L 0 0 L 112 0 L 112 50 L 0 50 L 0 25 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 25 L -4 0 C -4 0 -4 -4 0 -4 L 112 -4 C 112 -4 116 -4 116 0 L 116 50 C 116 50 116 54 112 54 L 0 54 C 0 54 -4 54 -4 50 L -4 25 Z" fill="none"/><foreignObject width="72" height="22" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(255, 245, 197); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 18px;" transform="matrix(1,0,0,1,20,14)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>极限定理</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,25)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="uNnxocgW8dNS2j4w0J_j2" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-284,2256.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>收敛性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs48d21cjn40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-442,2104.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分布函数收敛性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs48d7421x40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-558,2104.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>弱收敛性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nsa5d4340" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-646,2070.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4no36fs680" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1206,2056.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, 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style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)}</span></span></span></span></span>，如果存在一个非降函数F(x)使<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">lim_{n \to \infty} F_n(x) = F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>，在F(x)的每一个连续点处都成立</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nqiam2s80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1602,2064.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 21.5 L 0 0 L 356 0 L 356 43 L 0 43 L 0 21.5 Z"/><path d="M 0 21.5 L 0 8 C 0 8 0 0 8 0 L 348 0 C 348 0 356 0 356 8 L 356 35 C 356 35 356 43 348 43 L 8 43 C 8 43 0 43 0 35 L 0 21.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 21.5 L -4 0 C -4 0 -4 -4 0 -4 L 356 -4 C 356 -4 360 -4 360 0 L 360 43 C 360 43 360 47 356 47 L 0 47 C 0 47 -4 47 -4 43 L -4 21.5 Z" fill="none"/><foreignObject width="336" height="29" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_n(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>弱收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>，并记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mi>W</mi></mover></mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_n(x) \stackrel{W}{\longrightarrow} F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5393em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2893em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">W</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cs4nsbv7icg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-646,2138.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>引理</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nsgegbaw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1206,2124.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>设<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ F_n(x) \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)}</span></span></span></span></span>是实变量x的非降函数列，D是<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>R</mi><mn>1</mn></msup></mrow><annotation encoding="application/x-tex">R^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span>上的稠密集，若对D中的所有点，序列<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ F_n(x) \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)}</span></span></span></span></span>收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4ntsnw7kg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1595,2135.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 349 0 L 349 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 341 0 C 341 0 349 0 349 8 L 349 28 C 349 28 349 36 341 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 349 -4 C 349 -4 353 -4 353 0 L 353 36 C 353 36 353 40 349 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="329" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>则对<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>的一切连续点x有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">lim_{n \to \infty} F_n(x) = F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="Ucu9p0L1m7kPk8iIcw_wf" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-596,2223.6)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 272 0 L 272 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 264 0 C 264 0 272 0 272 8 L 272 23 C 272 23 272 31 264 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 272 -4 C 272 -4 276 -4 276 0 L 276 31 C 276 31 276 35 272 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="252" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>特征函数与分布函数的一一对应的连续性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4ntve5c940" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-712,2192.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>海莱定理</p></div></foreignObject></g><g data-node-id="cs4nu0xudc00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-858,2254.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 222 0 L 222 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 214 0 C 214 0 222 0 222 8 L 222 23 C 222 23 222 31 214 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 222 -4 C 222 -4 226 -4 226 0 L 226 31 C 226 31 226 35 222 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="202" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>莱维-克拉默定理（连续性定理）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nu8einzs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-988,2233.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>正极限定理</p></div></foreignObject></g><g data-node-id="cs4nuaxngxc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-988,2274.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>逆极限定理</p></div></foreignObject></g><g data-node-id="cs48dash5400" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-456,2408.1)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机变量的收敛性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs48e53z0800" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-586,2321.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>依分布收敛</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nv1iniw00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1176,2315.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 21.5 L 0 0 L 550 0 L 550 43 L 0 43 L 0 21.5 Z"/><path d="M 0 21.5 L 0 8 C 0 8 0 0 8 0 L 542 0 C 542 0 550 0 550 8 L 550 35 C 550 35 550 43 542 43 L 8 43 C 8 43 0 43 0 35 L 0 21.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 21.5 L -4 0 C -4 0 -4 -4 0 -4 L 550 -4 C 550 -4 554 -4 554 0 L 554 43 C 554 43 554 47 550 47 L 0 47 C 0 47 -4 47 -4 43 L -4 21.5 Z" fill="none"/><foreignObject width="530" height="29" x="0" y="0" class="text-obj formula-text" maxwidth="530px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 530px; max-width: 530px;"><p>设随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mtext>、</mtext><msub><mi>ξ</mi><mo stretchy="false">(</mo></msub><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi_n(\omega)、\xi_(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1052em;vertical-align:-0.3552em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mord cjk_fallback">、</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.5198em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mopen mtight">(</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3552em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>的分布函数分别为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_n(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>和<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>，如果<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mi>W</mi></mover></mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_n(x) \stackrel{W}{\longrightarrow} F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5393em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2893em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">W</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,21.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nwwcjyco0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1722,2315.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 21.5 L 0 0 L 506 0 L 506 43 L 0 43 L 0 21.5 Z"/><path d="M 0 21.5 L 0 8 C 0 8 0 0 8 0 L 498 0 C 498 0 506 0 506 8 L 506 35 C 506 35 506 43 498 43 L 8 43 C 8 43 0 43 0 35 L 0 21.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 21.5 L -4 0 C -4 0 -4 -4 0 -4 L 506 -4 C 506 -4 510 -4 510 0 L 510 43 C 510 43 510 47 506 47 L 0 47 C 0 47 -4 47 -4 43 L -4 21.5 Z" fill="none"/><foreignObject width="486" height="29" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ \xi_n(\omega) \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)}</span></span></span></span></span>依分布收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>，并记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mi>L</mi></mover></mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mi>d</mi></mover></mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi_n(x) \stackrel{L}{\longrightarrow} \xi(x)(\xi_n(x) \stackrel{d}{\longrightarrow} \xi(x))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5393em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2893em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">L</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.5471em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2971em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">))</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cs48ebb2cm80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-586,2374.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>依概率收敛</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nx1i5s680" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1050,2372.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 424 0 L 424 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 416 0 C 416 0 424 0 424 8 L 424 28 C 424 28 424 36 416 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 424 -4 C 424 -4 428 -4 428 0 L 428 36 C 428 36 428 40 424 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="404" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>如果对任意<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\varepsilon &gt;0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">ε</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，成立<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><mi>P</mi><mo stretchy="false">{</mo><mi mathvariant="normal">∣</mi><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>−</mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∣</mi><mo>≥</mo><mi>ε</mi><mo stretchy="false">}</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">lim_{n \to \infty} P \{ |\xi_n(\omega) - \xi(\omega)| \geq \varepsilon \} = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">{</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mord">∣</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">ε</span><span class="mclose">}</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4nytyan080" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1475,2368.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 21.5 L 0 0 L 385 0 L 385 43 L 0 43 L 0 21.5 Z"/><path d="M 0 21.5 L 0 8 C 0 8 0 0 8 0 L 377 0 C 377 0 385 0 385 8 L 385 35 C 385 35 385 43 377 43 L 8 43 C 8 43 0 43 0 35 L 0 21.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 21.5 L -4 0 C -4 0 -4 -4 0 -4 L 385 -4 C 385 -4 389 -4 389 0 L 389 43 C 389 43 389 47 385 47 L 0 47 C 0 47 -4 47 -4 43 L -4 21.5 Z" fill="none"/><foreignObject width="365" height="29" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ \xi_n(\omega) \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)}</span></span></span></span></span>依概率收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>，并记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mi>P</mi></mover></mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi_n(x) \stackrel{P}{\longrightarrow} \xi(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.5393em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2893em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cs48ei9i2e80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-563,2435.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 67 0 L 67 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 59 0 C 59 0 67 0 67 8 L 67 23 C 67 23 67 31 59 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 67 -4 C 67 -4 71 -4 71 0 L 71 31 C 71 31 71 35 67 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="47" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>r阶收敛</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4o0lyc7k00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1123,2421.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>设对随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ξ</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\xi_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>及<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mi mathvariant="normal">∣</mi><msub><mi>ξ</mi><mi>n</mi></msub><msup><mi mathvariant="normal">∣</mi><mi>r</mi></msup><mo>&lt;</mo><mi mathvariant="normal">∞</mi><mtext>，</mtext><mi>E</mi><mi mathvariant="normal">∣</mi><mi>ξ</mi><msup><mi mathvariant="normal">∣</mi><mi>r</mi></msup><mo>&lt;</mo><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">E|\xi_n|^r &lt; \infty，E|\xi|^r&lt; \infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">∞</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">∞</span></span></span></span></span>，其中r&gt;0为常数，如果<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><mi mathvariant="normal">∣</mi><msub><mi>ξ</mi><mi>n</mi></msub><mo>−</mo><mi>ξ</mi><msup><mi mathvariant="normal">∣</mi><mi>r</mi></msup><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">lim_{n \to \infty} |\xi_n - \xi|^r = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mord"><span class="mord">∣</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4o1kd5xig0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1431,2430.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 20 L 0 0 L 268 0 L 268 40 L 0 40 L 0 20 Z"/><path d="M 0 20 L 0 8 C 0 8 0 0 8 0 L 260 0 C 260 0 268 0 268 8 L 268 32 C 268 32 268 40 260 40 L 8 40 C 8 40 0 40 0 32 L 0 20 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 20 L -4 0 C -4 0 -4 -4 0 -4 L 268 -4 C 268 -4 272 -4 272 0 L 272 40 C 272 40 272 44 268 44 L 0 44 C 0 44 -4 44 -4 40 L -4 20 Z" fill="none"/><foreignObject width="248" height="26" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ \xi_n \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></span>r阶收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>，并记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ξ</mi><mi>n</mi></msub><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mi>r</mi></mover></mo><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi_n \stackrel{r}{\longrightarrow} \xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3068em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1124em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cs48emv27400" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-706,2494.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 210 0 L 210 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 202 0 C 202 0 210 0 210 8 L 210 23 C 210 23 210 31 202 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 210 -4 C 210 -4 214 -4 214 0 L 214 31 C 214 31 214 35 210 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="190" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>几乎处处收敛（以概率1收敛）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4o4a6tc0w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1009,2491.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 263 0 L 263 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 255 0 C 255 0 263 0 263 8 L 263 28 C 263 28 263 36 255 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 263 -4 C 263 -4 267 -4 267 0 L 267 36 C 267 36 267 40 263 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="243" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>如果<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">{</mo><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>=</mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P \{ lim_{n \to \infty} \xi_n(\omega) = \xi(\omega) \} = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">{</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)}</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cs4o4w28t6o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-1677,2489.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 20 L 0 0 L 628 0 L 628 40 L 0 40 L 0 20 Z"/><path d="M 0 20 L 0 8 C 0 8 0 0 8 0 L 620 0 C 620 0 628 0 628 8 L 628 32 C 628 32 628 40 620 40 L 8 40 C 8 40 0 40 0 32 L 0 20 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 20 L -4 0 C -4 0 -4 -4 0 -4 L 628 -4 C 628 -4 632 -4 632 0 L 632 40 C 632 40 632 44 628 44 L 0 44 C 0 44 -4 44 -4 40 L -4 20 Z" fill="none"/><foreignObject width="608" height="26" x="0" y="0" class="text-obj formula-text" maxwidth="608px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 608px; max-width: 608px;"><p>则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ \xi_n(\omega) \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)}</span></span></span></span></span>依概率1收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>，又称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{ \xi_n(\omega) \}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)}</span></span></span></span></span>几乎处处收敛于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>，并记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ξ</mi><mi>n</mi></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo><mover xmlns="http://www.w3.org/1999/xhtml"><mo><mo>⟶</mo></mo><mrow><mi>a</mi><mi mathvariant="normal">.</mi><mi>s</mi><mi mathvariant="normal">.</mi></mrow></mover></mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi_n(x) \stackrel{a.s.}{\longrightarrow} \xi(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3624em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.046em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1124em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">⟶</span></span></span><span style="top:-3.711em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span><span class="mord mtight">.</span><span class="mord mathnormal mtight">s</span><span class="mord mtight">.</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.011em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="Qo3g42aM-q9LVFkbD_Zyi" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-298,3011.6)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>大数定律</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path style="pointer-events: none;" d="M -7 0 L 7 0 Z"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;">42</text></g></g><g data-node-id="lv6BgpYivPAj1_saiUGfB" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,-326,4038.6)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>中心极限定理</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,-9,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path style="pointer-events: none;" d="M -7 0 L 7 0 Z"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;">46</text></g></g><g data-node-id="4dMjMLIV8XDQGx6RpF9cm" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,61.3,209.8)"><g fill="#FF9D17" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 102 L 0 0 L 198 0 L 198 204 L 0 204 L 0 102 Z"/><path d="M 0 102 L 0 0 L 198 0 L 198 204 L 0 204 L 0 102 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 102 L -4 0 C -4 0 -4 -4 0 -4 L 198 -4 C 198 -4 202 -4 202 0 L 202 204 C 202 204 202 208 198 208 L 0 208 C 0 208 -4 208 -4 204 L -4 102 Z" fill="none"/><foreignObject width="158" height="176" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(255, 255, 255); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 18px;" transform="matrix(1,0,0,1,20,14)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p style="text-align:center">默认使用</p><p style="text-align:center">希腊字母<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo separator="true">,</mo><mi>η</mi><mo separator="true">,</mo><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\xi,\eta,\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span></span></span></span>等</p><p style="text-align:center">表示随机变量</p><p style="text-align:center">无特殊说明</p><p style="text-align:center"><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>相当于X，取值记x</p><p style="text-align:center"><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi></mrow><annotation encoding="application/x-tex">\eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span></span></span></span>相当于Y，取值记y</p><p style="text-align:center"><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span></span></span></span>相当于Z，取值记z</p></div></foreignObject></g><g data-node-id="cr9ev4ywbz40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-7581.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>现象</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9ev6nmaww0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-7622.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>确定性（决定性）现象</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9evecv8l40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-7642.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>必然现象</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9evwsifxk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,972,-7642.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 230 0 L 230 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 222 0 C 222 0 230 0 230 8 L 230 23 C 230 23 230 31 222 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 230 -4 C 230 -4 234 -4 234 0 L 234 31 C 234 31 234 35 230 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="210" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在一定条件下，必然会发生的现象</p></div></foreignObject></g><g data-node-id="cr9evi0a0xs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-7601.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>不可能现象</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9ew3c7wa00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,986,-7601.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 244 0 L 244 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 236 0 C 236 0 244 0 244 8 L 244 23 C 244 23 244 31 236 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 244 -4 C 244 -4 248 -4 248 0 L 248 31 C 248 31 248 35 244 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="224" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在一定条件下，必然不会发生的现象</p></div></foreignObject></g><g data-node-id="cr9ewox7s3k0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-7540.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9ewqlvy680" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-7540.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 314 0 L 314 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 306 0 C 306 0 314 0 314 8 L 314 23 C 314 23 314 31 306 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 314 -4 C 314 -4 318 -4 318 0 L 318 31 C 318 31 318 35 314 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="294" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在一定的条件下，并不总是出现相同结果的现象</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,323,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9ex2dez1c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1126,-7560.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 412 0 L 412 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 404 0 C 404 0 412 0 412 8 L 412 23 C 412 23 412 31 404 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 412 -4 C 412 -4 416 -4 416 0 L 416 31 C 416 31 416 35 412 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="392" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在基本条件不变的情况下，一系列实验或观察会得到不同的结果</p></div></foreignObject></g><g data-node-id="cr9exkqpj2w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1126,-7519.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 496 0 L 496 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 488 0 C 488 0 496 0 496 8 L 496 23 C 496 23 496 31 488 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 496 -4 C 496 -4 500 -4 500 0 L 500 31 C 500 31 500 35 496 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="476" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>就个别实验，它会时而出现这种结果，时而出现那种结果，呈现出一种<strong>偶然性</strong></p></div></foreignObject></g><g data-node-id="cr9f43h8ueo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-7478.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机试验</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f44mghhk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-7478.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 370 0 L 370 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 362 0 C 362 0 370 0 370 8 L 370 23 C 370 23 370 31 362 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 370 -4 C 370 -4 374 -4 374 0 L 374 31 C 374 31 374 35 370 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="350" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对在相同条件下可以重复的随机现象的观察、记录、实验</p></div></foreignObject></g><g data-node-id="cr9f0ff39ao0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-6971.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>（随机）<strong>事件</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gi8ykti80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,712,-7351.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gbg6t4dk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,800,-7393.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本点角度定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f76usdeo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-7393.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 384 0 L 384 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 376 0 C 376 0 384 0 384 8 L 384 23 C 384 23 384 31 376 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 384 -4 C 384 -4 388 -4 388 0 L 388 31 C 388 31 388 35 384 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="364" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象的<strong>某些</strong>样本点组成的集合称为<strong>随机事件</strong>，简称<strong>事件</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,393,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gdgmxmfc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,-7437.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>单个点是一个集合</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9ggulmlhs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1554,-7437.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>基本事件</p></div></foreignObject></g><g data-node-id="cr9gdmflrg80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,-7396.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 462 0 L 462 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 454 0 C 454 0 462 0 462 8 L 462 26 C 462 26 462 34 454 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 462 -4 C 462 -4 466 -4 466 0 L 466 34 C 466 34 466 38 462 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="442" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>不包含任何点的集合也是一个集合（样本空间最大的子集），记为空集<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∅</mi></mrow><annotation encoding="application/x-tex">\emptyset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,471,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gepanqsg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1884,-7395.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>不可能事件</p></div></foreignObject></g><g data-node-id="cr9gdsuzvfk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,-7352.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 354 0 L 354 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 346 0 C 346 0 354 0 354 8 L 354 26 C 354 26 354 34 346 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 354 -4 C 354 -4 358 -4 358 0 L 358 34 C 358 34 358 38 354 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="334" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本空间是一个集合（样本空间最小的子集），记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,363,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gf3g1fqg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1776,-7351.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>必然事件</p></div></foreignObject></g><g data-node-id="cr9gfshus940" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2004,-7374)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 272 0 L 272 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 264 0 C 264 0 272 0 272 8 L 272 23 C 272 23 272 31 264 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 272 -4 C 272 -4 276 -4 276 0 L 276 31 C 276 31 276 35 272 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="252" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>作为随机事件的两个极端情形来统一处理</p></div></foreignObject></g><g data-node-id="cr9gbdokevc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,800,-7308.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象角度定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f0hpv0u00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,972,-7308.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 637 0 L 637 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 629 0 C 629 0 637 0 637 8 L 637 23 C 637 23 637 31 629 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 637 -4 C 637 -4 641 -4 641 0 L 641 31 C 641 31 641 35 637 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="617" height="17" x="0" y="0" class="text-obj" maxwidth="617px" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 617px; max-width: 617px;"><p>对于随机现象通常关心的是在试验或观察中某个结果是否出现，在这种结果称为<strong>随机事件</strong>，简称<strong>事件</strong></p></div></foreignObject></g><g data-node-id="cr9gihuxk280" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,712,-7030.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件间的运算</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gjqtrdps0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-7265.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 34 0 L 34 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 26 0 C 26 0 34 0 34 8 L 34 23 C 34 23 34 31 26 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 34 -4 C 34 -4 38 -4 38 0 L 38 31 C 38 31 38 35 34 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="14" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>并</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,43,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gsgq2tls0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-7265.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 417 0 L 417 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 409 0 C 409 0 417 0 417 8 L 417 23 C 417 23 417 31 409 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 417 -4 C 417 -4 421 -4 421 0 L 421 31 C 421 31 421 35 417 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="397" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>由事件A与B中所有的样本点（相同的只计入一次）组成的新事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,426,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gsgq3cg80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1387,-7265.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 193 0 L 193 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 185 0 C 185 0 193 0 193 8 L 193 23 C 193 23 193 31 185 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 193 -4 C 193 -4 197 -4 197 0 L 197 31 C 197 31 197 35 193 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="173" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件A与B中至少有一个发生</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,202,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gt0c28t40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1620,-7267.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 65 0 L 65 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 57 0 C 57 0 65 0 65 8 L 65 28 C 65 28 65 36 57 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 65 -4 C 65 -4 69 -4 69 0 L 69 36 C 69 36 69 40 65 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="45" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∪</mo><mi>B</mi></mrow><annotation encoding="application/x-tex">A\cup B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9gjrzhoc00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-7219.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 34 0 L 34 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 26 0 C 26 0 34 0 34 8 L 34 23 C 34 23 34 31 26 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 34 -4 C 34 -4 38 -4 38 0 L 38 31 C 38 31 38 35 34 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="14" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>交</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,43,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gtvfktdc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-7219.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 277 0 L 277 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 269 0 C 269 0 277 0 277 8 L 277 23 C 277 23 277 31 269 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 277 -4 C 277 -4 281 -4 281 0 L 281 31 C 281 31 281 35 277 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="257" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>由事件A与B中公共的样本点组成的新事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,286,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gu0j63xc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1247,-7219.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 137 0 L 137 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 129 0 C 129 0 137 0 137 8 L 137 23 C 137 23 137 31 129 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 137 -4 C 137 -4 141 -4 141 0 L 141 31 C 141 31 141 35 137 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="117" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件A与B同时发生</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,146,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gu6z9g9s0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1424,-7221.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 105 0 L 105 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 97 0 C 97 0 105 0 105 8 L 105 28 C 105 28 105 36 97 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 105 -4 C 105 -4 109 -4 109 0 L 109 36 C 109 36 109 40 105 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="85" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mo stretchy="false">(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">AB(A \cap B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9gjucvr9s0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-7173.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 34 0 L 34 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 26 0 C 26 0 34 0 34 8 L 34 23 C 34 23 34 31 26 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 34 -4 C 34 -4 38 -4 38 0 L 38 31 C 38 31 38 35 34 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="14" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>差</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,43,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gujagxyo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-7173.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 309 0 L 309 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 301 0 C 301 0 309 0 309 8 L 309 23 C 309 23 309 31 301 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 309 -4 C 309 -4 313 -4 313 0 L 313 31 C 313 31 313 35 309 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="289" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>由在事件A 中而不在B中的样本点组成的新事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,318,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9guki75ts0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1279,-7173.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 179 0 L 179 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 171 0 C 171 0 179 0 179 8 L 179 23 C 179 23 179 31 171 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 179 -4 C 179 -4 183 -4 183 0 L 183 31 C 183 31 183 35 179 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="159" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件A发生而事件B不发生</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,188,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gurum9e00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1498,-7175.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 136 0 L 136 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 128 0 C 128 0 136 0 136 8 L 136 28 C 136 28 136 36 128 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 136 -4 C 136 -4 140 -4 140 0 L 140 36 C 140 36 140 40 136 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="116" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>−</mo><mi>B</mi><mo>=</mo><mi>A</mi><mo>∩</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">A- B=A\cap\overline{B}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9gjv54rnc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-7045.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>逆（对立事件）</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9guw76djc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1014,-7047.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 280 0 L 280 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 272 0 C 272 0 280 0 280 8 L 280 26 C 280 26 280 34 272 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 280 -4 C 280 -4 284 -4 284 0 L 284 34 C 284 34 284 38 280 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="260" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>由在<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>中而不在A中的样本点组成的新事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,289,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gva81q2w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1334,-7045.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 100 0 L 100 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 92 0 C 92 0 100 0 100 8 L 100 23 C 100 23 100 31 92 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 100 -4 C 100 -4 104 -4 104 0 L 104 31 C 104 31 104 35 100 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="80" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件A不发生</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,109,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gvdxlygo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1474,-7106.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 101 0 L 101 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 93 0 C 93 0 101 0 101 8 L 101 28 C 101 28 101 36 93 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 101 -4 C 101 -4 105 -4 105 0 L 105 36 C 105 36 105 40 101 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="81" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mi mathvariant="normal">Ω</mi><mo>−</mo><mi>A</mi></mrow><annotation encoding="application/x-tex">\overline{A}=\Omega-A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord">Ω</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,110,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h1ojw78g0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1615,-7129.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 99 0 L 99 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 91 0 C 91 0 99 0 99 8 L 99 28 C 99 28 99 36 91 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 99 -4 C 99 -4 103 -4 103 0 L 103 36 C 103 36 103 40 99 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="79" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∪</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">A\cup\overline{A}=\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9h22h1ucw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1615,-7083.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 95 0 L 95 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 87 0 C 87 0 95 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class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9gvty0arc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1474,-7037.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 19.5 L 0 0 L 68 0 L 68 39 L 0 39 L 0 19.5 Z"/><path d="M 0 19.5 L 0 8 C 0 8 0 0 8 0 L 60 0 C 60 0 68 0 68 8 L 68 31 C 68 31 68 39 60 39 L 8 39 C 8 39 0 39 0 31 L 0 19.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 19.5 L -4 0 C -4 0 -4 -4 0 -4 L 68 -4 C 68 -4 72 -4 72 0 L 72 39 C 72 39 72 43 68 43 L 0 43 C 0 43 -4 43 -4 39 L -4 19.5 Z" fill="none"/><foreignObject width="48" height="25" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo stretchy="true">‾</mo></mover><mo>=</mo><mi>A</mi></mrow><annotation encoding="application/x-tex">\overline{\overline{A}}=A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span><span style="top:-4.0033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9gvyvod9c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1474,-6988.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 64 0 L 64 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 56 0 C 56 0 64 0 64 8 L 64 26 C 64 26 64 34 56 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 64 -4 C 64 -4 68 -4 68 0 L 68 34 C 68 34 68 38 64 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="44" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi mathvariant="normal">Ω</mi><mo stretchy="true">‾</mo></mover><mo>=</mo><mi mathvariant="normal">∅</mi></mrow><annotation encoding="application/x-tex">\overline{\Omega}=\emptyset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">Ω</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,73,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gxowp7zc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1578,-6988.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 64 0 L 64 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 56 0 C 56 0 64 0 64 8 L 64 27 C 64 27 64 35 56 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C 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class="vlist-r"><span class="vlist" style="height:0.95em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">∅</span></span></span><span style="top:-3.87em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.0556em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9h107vg7c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-6941.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 34 0 L 34 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 26 0 C 26 0 34 0 34 8 L 34 23 C 34 23 34 31 26 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 34 -4 C 34 -4 38 -4 38 0 L 38 31 C 38 31 38 35 34 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="14" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>和</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,43,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h118r2h40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-6941.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" 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transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 67 0 L 67 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 59 0 C 59 0 67 0 67 8 L 67 28 C 67 28 67 36 59 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 67 -4 C 67 -4 71 -4 71 0 L 71 36 C 71 36 71 40 67 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="47" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>+</mo><mi>B</mi></mrow><annotation encoding="application/x-tex">A+B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9h9g3o3uo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-6796.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>运算律</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h2gleso00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-6871.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 163 0 L 163 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 155 0 C 155 0 163 0 163 8 L 163 23 C 163 23 163 31 155 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 163 -4 C 163 -4 167 -4 167 0 L 167 31 C 167 31 167 35 163 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="143" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>德·摩根律（对偶原则）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,172,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h3z9wuzk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1161,-6871.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 198 0 L 198 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 190 0 C 190 0 198 0 198 8 L 198 23 C 198 23 198 31 190 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 198 -4 C 198 -4 202 -4 202 0 L 202 31 C 202 31 202 35 198 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="178" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>并（交）的逆=逆的交（并）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,207,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h48zpsc80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1399,-6896.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 134 0 L 134 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 126 0 C 126 0 134 0 134 8 L 134 26 C 134 26 134 34 126 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 134 -4 C 134 -4 138 -4 138 0 L 138 34 C 138 34 138 38 134 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="114" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>A</mi><mo>∪</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>∩</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{A \cup B}=\overline{A}\cap\overline{B}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,143,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h6vsmedk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1573,-6897.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 158 0 L 158 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 150 0 C 150 0 158 0 158 8 L 158 29 C 158 29 158 37 150 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 158 -4 C 158 -4 162 -4 162 0 L 162 37 C 162 37 162 41 158 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="138" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><msubsup><mo>⋃</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><msubsup><mo>⋂</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\overline{\bigcup_{i=1}^n A_i}=\bigcap_{i=1}^n \overline{A}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.304em;vertical-align:-0.2997em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0043em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.9243em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.183em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋂</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,167,18.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h86vuv1c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1771,-6897.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 158 0 L 158 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 150 0 C 150 0 158 0 158 8 L 158 29 C 158 29 158 37 150 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 158 -4 C 158 -4 162 -4 162 0 L 162 37 C 162 37 162 41 158 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="138" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><msubsup><mo>⋃</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><msubsup><mo>⋂</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\overline{\bigcup_{i=1}^{\infty}A_i}=\bigcap_{i=1}^{\infty} \overline{A}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.304em;vertical-align:-0.2997em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0043em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.9243em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.183em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋂</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9h4ytr0g00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1399,-6849.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 134 0 L 134 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 126 0 C 126 0 134 0 134 8 L 134 26 C 134 26 134 34 126 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 134 -4 C 134 -4 138 -4 138 0 L 138 34 C 138 34 138 38 134 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="114" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>A</mi><mo>∩</mo><mi>B</mi></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>∪</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{A \cap B}=\overline{A}\cup\overline{B}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,143,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h7yusa0o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1573,-6850.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 158 0 L 158 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 150 0 C 150 0 158 0 158 8 L 158 29 C 158 29 158 37 150 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 158 -4 C 158 -4 162 -4 162 0 L 162 37 C 162 37 162 41 158 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="138" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><msubsup><mo>⋂</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><msubsup><mo>⋃</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\overline{\bigcap_{i=1}^n A_i}=\bigcup_{i=1}^n \overline{A}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.304em;vertical-align:-0.2997em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0043em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋂</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.9243em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.183em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,167,18.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h8pj6fyw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1771,-6850.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 158 0 L 158 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 150 0 C 150 0 158 0 158 8 L 158 29 C 158 29 158 37 150 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 158 -4 C 158 -4 162 -4 162 0 L 162 37 C 162 37 162 41 158 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="138" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><msubsup><mo>⋂</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub></mrow><mo stretchy="true">‾</mo></mover><mo>=</mo><msubsup><mo>⋃</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\overline{\bigcap_{i=1}^{\infty}A_i}=\bigcup_{i=1}^{\infty} \overline{A}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.304em;vertical-align:-0.2997em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0043em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋂</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.9243em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.183em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9h9isybko0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-6803.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>交换律</p></div></foreignObject></g><g data-node-id="cr9h9k507rc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-6762.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>结合律</p></div></foreignObject></g><g data-node-id="cr9h9lgctg80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-6721.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分配律</p></div></foreignObject></g><g data-node-id="cr9h3iw7p2g0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1744,-7104)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>运算顺序</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h3m73lr40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1860,-7104)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>先逆后交再并差</p></div></foreignObject></g><g data-node-id="cr9gidpfv680" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,712,-6591.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件间的关系</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gis9cag00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-6678.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>包含关系</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gqplglpc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,972,-6678.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 165 0 L 165 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 157 0 C 157 0 165 0 165 8 L 165 23 C 165 23 165 31 157 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 165 -4 C 165 -4 169 -4 169 0 L 169 31 C 169 31 169 35 165 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="145" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>属于A的样本点必属于B</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,174,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9glp6sazs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1177,-6680.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 554 0 L 554 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 546 0 C 546 0 554 0 554 8 L 554 28 C 554 28 554 36 546 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 554 -4 C 554 -4 558 -4 558 0 L 558 36 C 558 36 558 40 554 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="534" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="534px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 534px; max-width: 534px;"><p>A的每个样本点都包含在B中，则称A<strong>包含于</strong>B（<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>⊂</mo><mi>B</mi></mrow><annotation encoding="application/x-tex">A \subset B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊂</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span>），亦称B<strong>包含</strong>了A（<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mo>⊃</mo><mi>A</mi></mrow><annotation encoding="application/x-tex">B \supset A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊃</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span></span>）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,563,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gnph7xw80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1771,-6680.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 191 0 L 191 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 183 0 C 183 0 191 0 191 8 L 191 28 C 191 28 191 36 183 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 191 -4 C 191 -4 195 -4 195 0 L 195 36 C 195 36 195 40 191 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="171" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∀</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">\forall A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">∀</span><span class="mord mathnormal">A</span></span></span></span></span>，必有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∅</mi><mo>⊂</mo><mi>A</mi><mo>⊂</mo><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\emptyset \subset A \subset \Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊂</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊂</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9giz3otlk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-6632.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>等价（相等）关系</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gqejjh480" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1028,-6632.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 351 0 L 351 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 343 0 C 343 0 351 0 351 8 L 351 23 C 351 23 351 31 343 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 351 -4 C 351 -4 355 -4 355 0 L 355 31 C 355 31 355 35 351 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="331" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>属于A的样本点必属于B，而且属于B的样本点必属于A</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,360,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gp08t3j40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1419,-6634.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 554 0 L 554 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 546 0 C 546 0 554 0 554 8 L 554 28 C 554 28 554 36 546 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 554 -4 C 554 -4 558 -4 558 0 L 558 36 C 558 36 558 40 554 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="534" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="534px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 534px; max-width: 534px;"><p>A包含B，同时B包含A，则称事件A与事件B等价，或称事件A等于事件B，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>=</mo><mi>B</mi></mrow><annotation encoding="application/x-tex">A=B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9gjcnmgps0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-6568.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>互不相容</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gr14s0zk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,972,-6568.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 393 0 L 393 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 385 0 C 385 0 393 0 393 8 L 393 23 C 393 23 393 31 385 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 393 -4 C 393 -4 397 -4 397 0 L 397 31 C 397 31 397 35 393 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="373" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>如果A与B没有相同的样本点，事件A与事件B不可能同时发生</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,402,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9grfa5euw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1405,-6570.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 194 0 L 194 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 186 0 C 186 0 194 0 194 8 L 194 28 C 194 28 194 36 186 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 194 -4 C 194 -4 198 -4 198 0 L 198 36 C 198 36 198 40 194 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="174" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mo>=</mo><mi mathvariant="normal">∅</mi></mrow><annotation encoding="application/x-tex">AB=\emptyset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></span>，称A与B互不相容</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,203,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9gs1kn1cw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1639,-6588.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 174 0 L 174 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 166 0 C 166 0 174 0 174 8 L 174 23 C 174 23 174 31 166 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 174 -4 C 174 -4 178 -4 178 0 L 178 31 C 178 31 178 35 174 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="154" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本点之间是互不相容的</p></div></foreignObject></g><g data-node-id="cr9gzmcpgk80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1639,-6547.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 216 0 L 216 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 208 0 C 208 0 216 0 216 8 L 216 23 C 216 23 216 31 208 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 216 -4 C 216 -4 220 -4 220 0 L 220 31 C 220 31 220 35 216 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="196" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>互不相容事件不一定是对立事件</p></div></foreignObject></g><g data-node-id="crifpqz566o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,856,-6504.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对立</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crifqmi1ta00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,944,-6505.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 280 0 L 280 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 272 0 C 272 0 280 0 280 8 L 280 26 C 280 26 280 34 272 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 280 -4 C 280 -4 284 -4 284 0 L 284 34 C 284 34 284 38 280 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="260" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>由在<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>中而不在A中的样本点组成的新事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,289,17)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crifqpy1p7k0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1264,-6506.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 184 0 L 184 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 176 0 C 176 0 184 0 184 8 L 184 28 C 184 28 184 36 176 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 184 -4 C 184 -4 188 -4 188 0 L 188 36 C 188 36 188 40 184 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="164" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∩</mo><mi>B</mi><mo>=</mo><mi mathvariant="normal">∅</mi><mo separator="true">,</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo>=</mo><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">A \cap B=\emptyset,A \cup B =\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∩</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord">∅</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,193,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crifqmi2pog0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1488,-6504.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 216 0 L 216 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 208 0 C 208 0 216 0 216 8 L 216 23 C 216 23 216 31 208 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 216 -4 C 216 -4 220 -4 220 0 L 220 31 C 220 31 220 35 216 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="196" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对立事件一定是互不相容的事件</p></div></foreignObject></g><g data-node-id="cr9h5qrlkm80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2008,-6885)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>图形直观表示</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9h5yhjbhk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2152,-6885)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 68 0 L 68 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 60 0 C 60 0 68 0 68 8 L 68 23 C 68 23 68 31 60 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 68 -4 C 68 -4 72 -4 72 0 L 72 31 C 72 31 72 35 68 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="48" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>Venn图</p></div></foreignObject></g><g data-node-id="cr9f9u967e00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-6458.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>样本点</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f8snykko0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,670,-6460.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 259 0 L 259 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 251 0 C 251 0 259 0 259 8 L 259 28 C 259 28 259 36 251 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 259 -4 C 259 -4 263 -4 263 0 L 263 36 C 263 36 263 40 259 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="239" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机试验可能出现的基本结果，记为 <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9erq72kmg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-6294.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong style="color:#f44f3b">样本空间</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f7uz0fnk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-6414.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 465 0 L 465 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 457 0 C 457 0 465 0 465 8 L 465 28 C 465 28 465 36 457 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 465 -4 C 465 -4 469 -4 469 0 L 469 36 C 469 36 469 40 465 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="445" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象的一切可能基本结果组成的集合称为样本空间，记为 <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mo>=</mo><mrow><mo fence="true">{</mo><mi>ω</mi><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">\Omega=\left\{ \omega \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9fzsjexs00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-6339.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>注意</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fztuins00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-6368.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 272 0 L 272 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 264 0 C 264 0 272 0 272 8 L 272 23 C 272 23 272 31 264 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 272 -4 C 272 -4 276 -4 276 0 L 276 31 C 276 31 276 35 272 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="252" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本空间中的元素可以是数也可以不是数</p></div></foreignObject></g><g data-node-id="cr9g0dn54v40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-6327.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象的样本空间<strong>至少有两个样本点</strong>，如果将确定性现象放在一起考虑，则<strong>含有一个样本点的样本空间对应的为确定性现象</strong></p></div></foreignObject></g><g data-node-id="cr9g0pk59i80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-6249.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分类</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9g2ktf8xc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-6269.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>离散样本空间</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9g25czdig0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,916,-6269.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 202 0 L 202 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 194 0 C 194 0 202 0 202 8 L 202 23 C 202 23 202 31 194 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 202 -4 C 202 -4 206 -4 206 0 L 206 31 C 206 31 206 35 202 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="182" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本点的个数为有限个或可列</p></div></foreignObject></g><g data-node-id="cr9g2nirwww0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-6228.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>连续样本空间</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9g25d05yg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,916,-6228.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 202 0 L 202 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 194 0 C 194 0 202 0 202 8 L 202 23 C 202 23 202 31 194 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 202 -4 C 202 -4 206 -4 206 0 L 206 31 C 206 31 206 35 202 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="182" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本点的个数为不可列无限个</p></div></foreignObject></g><g data-node-id="crigp7friqw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-6175.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本空间的分割</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigpbg6au00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-6187.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 28 L 0 0 L 722 0 L 722 56 L 0 56 L 0 28 Z"/><path d="M 0 28 L 0 8 C 0 8 0 0 8 0 L 714 0 C 714 0 722 0 722 8 L 722 48 C 722 48 722 56 714 56 L 8 56 C 8 56 0 56 0 48 L 0 28 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 28 L -4 0 C -4 0 -4 -4 0 -4 L 722 -4 C 722 -4 726 -4 726 0 L 726 56 C 726 56 726 60 722 60 L 0 60 C 0 60 -4 60 -4 56 L -4 28 Z" fill="none"/><foreignObject width="702" height="42" x="0" y="0" class="text-obj formula-text" maxwidth="702px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 702px; max-width: 702px;"><p>对样本空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>，如果有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>D</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>D</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">D_1,D_2,\dots,D_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>满足：诸<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">D_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>互不相容，且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>⋃</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>D</mi><mi>i</mi></msub><mo>=</mo><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\bigcup_{n=1}^{\infty} D_i = \Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>，则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>D</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>D</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>D</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">D_1,D_2,\dots,D_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>为样本空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>的一组分割，亦可推广到可列个互不相容事件组成一组分割的情况</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,731,28)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigsd5w1ps0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1604,-6175.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 384 0 L 384 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 376 0 C 376 0 384 0 384 8 L 384 23 C 384 23 384 31 376 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 384 -4 C 384 -4 388 -4 388 0 L 388 31 C 388 31 388 35 384 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="364" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>实际处理问题时，利用样本空间的分割可以简化问题的处理</p></div></foreignObject></g><g data-node-id="crifxjxya3k0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-5980.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong style="color:#f44f3b">事件域</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crifyr3265k0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,670,-6074.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 336 0 L 336 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 328 0 C 328 0 336 0 336 8 L 336 27 C 336 27 336 35 328 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C -4 0 -4 -4 0 -4 L 336 -4 C 336 -4 340 -4 340 0 L 340 35 C 340 35 340 39 336 39 L 0 39 C 0 39 -4 39 -4 35 L -4 17.5 Z" fill="none"/><foreignObject width="316" height="21" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>设<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>是一个样本空间，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>是<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>的一些子集构成的集类</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,345,17.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crig02013800" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1046,-6121.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 64 0 L 64 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 56 0 C 56 0 64 0 64 8 L 64 27 C 64 27 64 35 56 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C -4 0 -4 -4 0 -4 L 64 -4 C 64 -4 68 -4 68 0 L 68 35 C 68 35 68 39 64 39 L 0 39 C 0 39 -4 39 -4 35 L -4 17.5 Z" fill="none"/><foreignObject width="44" height="21" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\Omega \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord">Ω</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crig07fz3zk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1046,-6076.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 152 0 L 152 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 144 0 C 144 0 152 0 152 8 L 152 29 C 152 29 152 37 144 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 152 -4 C 152 -4 156 -4 156 0 L 156 37 C 156 37 156 41 152 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="132" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">A \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\overline{A} \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9224em;vertical-align:-0.0391em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crig0rcjc800" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1046,-6029.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 333 0 L 333 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 325 0 C 325 0 333 0 333 8 L 333 29 C 333 29 333 37 325 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 333 -4 C 333 -4 337 -4 337 0 L 337 37 C 337 37 337 41 333 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="313" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="313px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 313px; max-width: 313px;"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>n</mi></msub><mo>∈</mo><mi mathvariant="script">F</mi><mtext>，</mtext><mi>n</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">A_n \in \mathscr{F}，n=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>，则 <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>⋃</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>n</mi></msub><mo>=</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\bigcup_{n=1}^{\infty} A_n = \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crig1m1a4mw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1409,-6076)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 248 0 L 248 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 240 0 C 240 0 248 0 248 8 L 248 29 C 248 29 248 37 240 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 248 -4 C 248 -4 252 -4 252 0 L 252 37 C 252 37 252 41 248 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="228" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>为一个事件域，也称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>代数或<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>域</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,257,18.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crig2kyrhpc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1697,-6095)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 363 0 L 363 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 355 0 C 355 0 363 0 363 8 L 363 26 C 363 26 363 34 355 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 363 -4 C 363 -4 367 -4 367 0 L 367 34 C 367 34 367 38 363 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="343" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对逆、并、交、差的可列次运算封闭，并且包含了<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>和<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∅</mi></mrow><annotation encoding="application/x-tex">\emptyset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crig6z81zfk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1697,-6051)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本点并不一定是事件</p></div></foreignObject></g><g data-node-id="crigctuvq280" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,670,-5982.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29.5 L 0 0 L 520 0 L 520 59 L 0 59 L 0 29.5 Z"/><path d="M 0 29.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 51 C 520 51 520 59 512 59 L 8 59 C 8 59 0 59 0 51 L 0 29.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 59 C 524 59 524 63 520 63 L 0 63 C 0 63 -4 63 -4 59 L -4 29.5 Z" fill="none"/><foreignObject width="500" height="45" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mn>1</mn></msup></mrow><annotation encoding="application/x-tex">\mathbb{R}^1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span>记数直线或实数全体，并称由一切形为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">[a,b)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span></span></span></span></span>的有界左闭右开区间构成的集类所产生的<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>域为一维博雷尔<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>域，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">B</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\mathscr{B}_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.04087em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0409em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>，称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">B</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\mathscr{B}_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.04087em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0409em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>中的集为一维博雷尔点集</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crighou2we00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1230,-5977.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>包含一切开区间、闭区间、单点集、可列集，以及由它们经过可列次逆、并、交运算而得出的集合【相当大的一个集合】</p></div></foreignObject></g><g data-node-id="crigk01dqe80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,670,-5913.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29.5 L 0 0 L 520 0 L 520 59 L 0 59 L 0 29.5 Z"/><path d="M 0 29.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 51 C 520 51 520 59 512 59 L 8 59 C 8 59 0 59 0 51 L 0 29.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 59 C 524 59 524 63 520 63 L 0 63 C 0 63 -4 63 -4 59 L -4 29.5 Z" fill="none"/><foreignObject width="500" height="45" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">\mathbb{R}^n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6889em;"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span></span></span></span>记n维欧几里得空间，并称由一切n维矩形构成的集类所产生的<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>域为n维博雷尔<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>域，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">B</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\mathscr{B}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.04087em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0409em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>，称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">B</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\mathscr{B}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.04087em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0409em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>中的集为n维博雷尔点集</p></div></foreignObject></g><g data-node-id="cr9fdsa0c600" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-5508.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong style="color:#f44f3b">概率</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fg30b9r40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-5735.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fdti75a80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5844.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 590 0 L 590 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 582 0 C 582 0 590 0 590 8 L 590 23 C 590 23 590 31 582 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 590 -4 C 590 -4 594 -4 594 0 L 594 31 C 594 31 594 35 590 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="570" height="17" x="0" y="0" class="text-obj" maxwidth="570px" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 570px; max-width: 570px;"><p>对于随机事件A，用一个数P(A)来表示该事件发生的可能性大小，这个数称为随机事件的概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,599,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9feidc3so0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1374,-5844.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 230 0 L 230 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 222 0 C 222 0 230 0 230 8 L 230 23 C 230 23 230 31 222 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 230 -4 C 230 -4 234 -4 234 0 L 234 31 C 234 31 234 35 230 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="210" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>度量了<strong>随机事件发生的可能性大小</strong></p></div></foreignObject></g><g data-node-id="cr9hj7chl600" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5801.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>样本点角度定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9hjbmpbds0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-5801.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 319 0 L 319 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 311 0 C 311 0 319 0 319 8 L 319 23 C 319 23 319 31 311 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 319 -4 C 319 -4 323 -4 323 0 L 323 31 C 323 31 323 35 319 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="299" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>任何事件A的概率P(A)是A中各样本点的概率之和</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,328,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9hjwdz1wg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1261,-5803.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 233 0 L 233 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 225 0 C 225 0 233 0 233 8 L 233 28 C 233 28 233 36 225 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 233 -4 C 233 -4 237 -4 237 0 L 237 36 C 237 36 237 40 233 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="213" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>则有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\Omega)=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">Ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>≤</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">0\leq P(A)\leq1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crigt8xq4v40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5739.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 269 0 L 269 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 261 0 C 261 0 269 0 269 8 L 269 27 C 269 27 269 35 261 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C -4 0 -4 -4 0 -4 L 269 -4 C 269 -4 273 -4 273 0 L 273 35 C 273 35 273 39 269 39 L 0 39 C 0 39 -4 39 -4 35 L -4 17.5 Z" fill="none"/><foreignObject width="249" height="21" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率是定义在事件域<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>上的一个集合函数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,278,17.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criguv081zc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1053,-5757.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 384 0 L 384 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 376 0 C 376 0 384 0 384 8 L 384 23 C 384 23 384 31 376 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 384 -4 C 384 -4 388 -4 388 0 L 388 31 C 388 31 388 35 384 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="364" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>古典概型中，概率通过有利场合数与可能结果总数之比定义</p></div></foreignObject></g><g data-node-id="crigvck10o00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1053,-5716.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 552 0 L 552 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 544 0 C 544 0 552 0 552 8 L 552 23 C 552 23 552 31 544 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 552 -4 C 552 -4 556 -4 556 0 L 556 31 C 556 31 556 35 552 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="532" height="17" x="0" y="0" class="text-obj" maxwidth="532px" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 532px; max-width: 532px;"><p>几何概型中，情况类似单它要求对可列个互不相容的事件之和有可加性（可列可加性）</p></div></foreignObject></g><g data-node-id="criguninz400" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5626.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>概率的公理化定义</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigvy1xy940" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,916,-5628.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 348 0 L 348 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 340 0 C 340 0 348 0 348 8 L 348 27 C 348 27 348 35 340 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C -4 0 -4 -4 0 -4 L 348 -4 C 348 -4 352 -4 352 0 L 352 35 C 352 35 352 39 348 39 L 0 39 C 0 39 -4 39 -4 35 L -4 17.5 Z" fill="none"/><foreignObject width="328" height="21" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义在事件域<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>上的一个集合函数P称为概率，它满足</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,357,17.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigx03kbug0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1304,-5675.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 191 0 L 191 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 183 0 C 183 0 191 0 191 8 L 191 29 C 191 29 191 37 183 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 191 -4 C 191 -4 195 -4 195 0 L 195 37 C 195 37 195 41 191 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="171" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(A) \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，对一切<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">A \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,200,18.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigyr174rs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1535,-5672.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>非负性</strong></p></div></foreignObject></g><g data-node-id="crigxetqv600" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1304,-5628.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 90 0 L 90 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 28 C 90 28 90 36 82 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 36 C 94 36 94 40 90 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="70" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\Omega) = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">Ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigyz5q4sw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1434,-5626.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>规范性（正则性）</strong></p></div></foreignObject></g><g data-node-id="crigxnq8ra80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1304,-5582.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 502 0 L 502 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 494 0 C 494 0 502 0 502 8 L 502 29 C 502 29 502 37 494 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 502 -4 C 502 -4 506 -4 506 0 L 506 37 C 506 37 506 41 502 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="482" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>i</mi></msub><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">A_i \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">i=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>且两两互不相容，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\sum_{i=1}^{\infty} A_i) = \sum_{i=1}^{\infty} P(A_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,511,18.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crigytuaeko0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1846,-5579.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>可列可加性</strong></p></div></foreignObject></g><g data-node-id="crigz9ja31c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-5282.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>性质</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crih1txa6z40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5535.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 154 0 L 154 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 146 0 C 146 0 154 0 154 8 L 154 23 C 154 23 154 31 146 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 154 -4 C 154 -4 158 -4 158 0 L 158 31 C 158 31 158 35 154 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="134" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>不可能事件的概率为0</p></div></foreignObject></g><g data-node-id="crih24t16ao0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5494.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 258 0 L 258 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 250 0 C 250 0 258 0 258 8 L 258 28 C 258 28 258 36 250 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 258 -4 C 258 -4 262 -4 262 0 L 262 36 C 262 36 262 40 258 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="238" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对任何事件A有：<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\overline{A})=1-P(A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1333em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crih2jy3n6w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5448.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 321 0 L 321 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 313 0 C 313 0 321 0 321 8 L 321 28 C 321 28 321 36 313 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 321 -4 C 321 -4 325 -4 325 0 L 325 36 C 325 36 325 40 321 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="301" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>如果<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>⊃</mo><mi>B</mi></mrow><annotation encoding="application/x-tex">A \supset B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊃</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo>−</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>−</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A-B)=P(A)-P(B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crihbho4zkw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5400.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>单调性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crih3f1aotk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,846,-5402.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 227 0 L 227 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 219 0 C 219 0 227 0 227 8 L 227 28 C 227 28 227 36 219 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 227 -4 C 227 -4 231 -4 231 0 L 231 36 C 231 36 231 40 227 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="207" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>如果<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>⊃</mo><mi>B</mi></mrow><annotation encoding="application/x-tex">A \supset B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊃</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>≥</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A) \geq P(B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crihbkp7fe80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5330.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>加法公式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crih3kjb1dk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,860,-5356.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 288 0 L 288 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 280 0 C 280 0 288 0 288 8 L 288 28 C 288 28 288 36 280 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 288 -4 C 288 -4 292 -4 292 0 L 292 36 C 292 36 292 40 288 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="268" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>−</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A \cup B) = P(A)+P(B)-P(AB)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crih40irry00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,860,-5310.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 1058 0 L 1058 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 1050 0 C 1050 0 1058 0 1058 8 L 1058 29 C 1058 29 1058 37 1050 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 1058 -4 C 1058 -4 1062 -4 1062 0 L 1062 37 C 1062 37 1062 41 1058 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="1038" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="1038px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 1038px; max-width: 1038px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo>∪</mo><msub><mi>A</mi><mn>2</mn></msub><mo>∪</mo><mo>⋯</mo><mo>∪</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow></msub><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>−</mo><msub><mo>∑</mo><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow></msub><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo></mrow><mo>+</mo><msub><mo>∑</mo><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow></msub><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><msub><mi>A</mi><mi>j</mi></msub><msub><mi>A</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mrow><mo>−</mo><mo>⋯</mo><mo>+</mo><mo stretchy="false">(</mo><mo>−</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>A</mi><mn>2</mn></msub><mo>…</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mtext>，</mtext><mi>i</mi><mo>&lt;</mo><mi>j</mi><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(A_1 \cup A_2 \cup \dots \cup A_n) = \sum_{i=1,\dots,n} P(A_i) - \sum_{i,j=1,\dots,n}{P(A_i A_j)}  + \sum_{i,j,k = 1,\dots,n}{P(A_iA_jA_k)} - \dots + (-1)^{n-1} P(A_1A_2\dots A_n)，i&lt;j&lt;k&lt;\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5556em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1858em;vertical-align:-0.4358em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.162em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="minner mtight">…</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4358em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1858em;vertical-align:-0.4358em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.162em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mrel mtight">=</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="minner mtight">…</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4358em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1858em;vertical-align:-0.4358em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1864em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="minner mtight">…</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4358em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">−</span><span class="mord">1</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord cjk_fallback">，</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.123em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crih9dsfia00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5261.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>布尔不等式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crih8oiopls0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,874,-5263.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 214 0 L 214 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 206 0 C 206 0 214 0 214 8 L 214 28 C 214 28 214 36 206 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 214 -4 C 214 -4 218 -4 218 0 L 218 36 C 218 36 218 40 214 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="194" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A \cup B) \leq P(A) + P(B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,223,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crihcjeo3ww0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1128,-5261.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 169 0 L 169 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 161 0 C 161 0 169 0 169 8 L 169 23 C 169 23 169 31 161 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 169 -4 C 169 -4 173 -4 173 0 L 173 31 C 173 31 173 35 169 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="149" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>可推广至n个事件的场合</p></div></foreignObject></g><g data-node-id="crih9oqo5280" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5215.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 133 0 L 133 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 125 0 C 125 0 133 0 133 8 L 133 23 C 133 23 133 31 125 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 133 -4 C 133 -4 137 -4 137 0 L 137 31 C 137 31 137 35 133 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="113" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>Bonferroni不等式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,142,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crih8zxxy400" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,917,-5217.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 225 0 L 225 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 217 0 C 217 0 225 0 225 8 L 225 28 C 225 28 225 36 217 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 225 -4 C 225 -4 229 -4 229 0 L 229 36 C 229 36 229 40 225 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="205" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo><mo>≥</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(AB) \geq P(A) + P(B) - 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,234,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crihcqoi6b40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1182,-5215.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 169 0 L 169 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 161 0 C 161 0 169 0 169 8 L 169 23 C 169 23 169 31 161 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 169 -4 C 169 -4 173 -4 173 0 L 173 31 C 173 31 173 35 169 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="149" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>可推广至n个事件的场合</p></div></foreignObject></g><g data-node-id="crih1yj4zrc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5169.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率具有有限可加性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,155,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criha2jpcyg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-5171.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 595 0 L 595 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 587 0 C 587 0 595 0 595 8 L 595 28 C 595 28 595 36 587 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 595 -4 C 595 -4 599 -4 599 0 L 599 36 C 599 36 599 40 595 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="575" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="575px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 575px; max-width: 575px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>i</mi></msub><msub><mi>A</mi><mi>j</mi></msub><mo>=</mo><mi mathvariant="normal">∅</mi><mo stretchy="false">(</mo><mi>i</mi><mo mathvariant="normal">≠</mo><mi>j</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">A_iA_j = \emptyset(i \neq j)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">∅</span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mclose">)</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo>+</mo><msub><mi>A</mi><mn>2</mn></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo>+</mo><mo>⋯</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_1+A_2+\dots+A_n) = P(A_1)+P(A_2)+\dots+P(A_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crihhldi4rk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5122.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率是下连续的</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crihic48d2o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-5125.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 672 0 L 672 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 664 0 C 664 0 672 0 672 8 L 672 29 C 672 29 672 37 664 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 672 -4 C 672 -4 676 -4 676 0 L 676 37 C 676 37 676 41 672 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="652" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="652px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 652px; max-width: 652px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">S_n = \sum_{i=1}^{n} A_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>，若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">S_n \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>，且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>S</mi><mi>n</mi></msub><mo>⊂</mo><msub><mi>S</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">S_n \subset S_{n+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊂</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8917em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">n=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><mi>P</mi><mo stretchy="false">(</mo><msub><mi>S</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><msub><mi>S</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">lim_{n \to \infty} P(S_n) = P(lim_{n \to \infty} S_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crihhrpzkko0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5075.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率是上连续的</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crihjjfkrrs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-5078.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 554 0 L 554 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 546 0 C 546 0 554 0 554 8 L 554 29 C 554 29 554 37 546 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 554 -4 C 554 -4 558 -4 558 0 L 558 37 C 558 37 558 41 554 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="534" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="534px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 534px; max-width: 534px;"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>i</mi></msub><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">B_i \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>，且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>i</mi></msub><mo>⊃</mo><msub><mi>B</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">B_i \supset B_{i+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⊃</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8917em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">i=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><mi>P</mi><mo stretchy="false">(</mo><msub><mi>B</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub><msub><mi>B</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">lim_{n \to \infty} P(B_n) = P(lim_{n \to \infty} B_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crihhuzunc00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-5029.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>次可加性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crihpaiiyhs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,860,-5031.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 213 0 L 213 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 205 0 C 205 0 213 0 213 8 L 213 28 C 213 28 213 36 205 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 213 -4 C 213 -4 217 -4 217 0 L 217 36 C 217 36 217 40 213 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="193" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msubsup><mo>⋃</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>≤</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\bigcup_{i=1}^{\infty}A_i) \leq \sum_{i=1}^{\infty} P(A_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crihqfusx800" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1604,-5146)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>可列可加</p></div></foreignObject></g><g data-node-id="cr9f5a7juw80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-4819.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>频率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9ffzndy2w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-4978.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f5herytc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,744,-4985.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 22.5 L 0 0 L 662 0 L 662 45 L 0 45 L 0 22.5 Z"/><path d="M 0 22.5 L 0 8 C 0 8 0 0 8 0 L 654 0 C 654 0 662 0 662 8 L 662 37 C 662 37 662 45 654 45 L 8 45 C 8 45 0 45 0 37 L 0 22.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 22.5 L -4 0 C -4 0 -4 -4 0 -4 L 662 -4 C 662 -4 666 -4 666 0 L 666 45 C 666 45 666 49 662 49 L 0 49 C 0 49 -4 49 -4 45 L -4 22.5 Z" fill="none"/><foreignObject width="642" height="31" x="0" y="0" class="text-obj formula-text" maxwidth="642px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 642px; max-width: 642px;"><p>对于随机事件A，若在N此实验中出现了n次，则称 <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mi>n</mi><mi>N</mi></mfrac></mstyle></mrow><annotation encoding="application/x-tex">F_N(A) = \dfrac{n}{N}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.7936em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">N</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span> 为随机事件A在N次试验中出现的频率</p></div></foreignObject></g><g data-node-id="cr9fg5rzmp40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-4844.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>基本性质</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fg7udwk00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4928.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>非负性</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fjhl3xu00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,874,-4930.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 100 0 L 100 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 92 0 C 92 0 100 0 100 8 L 100 28 C 100 28 100 36 92 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 100 -4 C 100 -4 104 -4 104 0 L 104 36 C 104 36 104 40 100 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="80" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">F_N(A)\geq0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9filhxqrk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4859.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 307 0 L 307 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 299 0 C 299 0 307 0 307 8 L 307 23 C 307 23 307 31 299 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 307 -4 C 307 -4 311 -4 311 0 L 311 31 C 311 31 311 35 307 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="287" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>任何随机事件在N次试验中出现的频率不大于1</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,316,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fhiq9nj40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1119,-4882.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 211 0 L 211 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 203 0 C 203 0 211 0 211 8 L 211 23 C 211 23 211 31 203 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 211 -4 C 211 -4 215 -4 215 0 L 215 31 C 215 31 215 35 211 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="191" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: normal;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>必然事件</strong>在N次实验中出现N次</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,220,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fgix82xk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1370,-4884.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 232 0 L 232 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 224 0 C 224 0 232 0 232 8 L 232 28 C 232 28 232 36 224 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 232 -4 C 232 -4 236 -4 236 0 L 236 36 C 236 36 236 40 232 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="212" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>以 <span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span> 记必然事件，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">F_N(\Omega)=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">Ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9fhrf8uko0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1119,-4836.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 222 0 L 222 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 214 0 C 214 0 222 0 222 8 L 222 23 C 222 23 222 31 214 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 222 -4 C 222 -4 226 -4 226 0 L 226 31 C 226 31 226 35 222 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="202" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>不可能事件</strong>在N次试验中出现0次</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,231,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criffzibz2g0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1381,-4838.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 230 0 L 230 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 222 0 C 222 0 230 0 230 8 L 230 28 C 230 28 230 36 222 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 230 -4 C 230 -4 234 -4 234 0 L 234 36 C 234 36 234 40 230 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="210" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∅</mi></mrow><annotation encoding="application/x-tex">\emptyset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></span>记不可能事件，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi mathvariant="normal">∅</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">F_N(\emptyset)=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">∅</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9fg9qe32w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4761.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>频率可加性</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fjs9xcyo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-4792.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 520 0 L 520 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 45 C 520 45 520 53 512 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 53 C 524 53 524 57 520 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="500" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若A与B是<strong>两个</strong>不会同时发生的随机事件，以A+B表示A或B至少出现其一这个事件，则有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_N(A+B)=F_N(A)+F_N(B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9fj2a88h40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-4729.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 370 0 L 370 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 362 0 C 362 0 370 0 370 8 L 370 23 C 370 23 370 31 362 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 370 -4 C 370 -4 374 -4 374 0 L 374 31 C 374 31 374 35 370 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="350" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于<strong>有限个</strong>两两不会同时发生的随机事件也有频率可加性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,379,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crifhivofa80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1312,-4729.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>有限可加性</p></div></foreignObject></g><g data-node-id="cr9f3uam7lc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,656,-4659.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>频率稳定性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9f4exrd8w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,786,-4688.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>虽然个别随机事件在某次试验或观察中可以出现也可以不出现，但在大量实验中它却呈现出明显的规律性——频率稳定性</p></div></foreignObject></g><g data-node-id="cr9far2pbds0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,786,-4630.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 556 0 L 556 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 548 0 C 548 0 556 0 556 8 L 556 23 C 556 23 556 31 548 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 556 -4 C 556 -4 560 -4 560 0 L 560 31 C 560 31 560 35 556 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="536" height="17" x="0" y="0" class="text-obj" maxwidth="536px" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 536px; max-width: 536px;"><p>测量值的平均值在<strong>某固定常数附近波动</strong>，诸测量值在此常数两旁的分布呈现某种<strong>对称性</strong></p></div></foreignObject></g><g data-node-id="cr9fbm6yups0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-4569.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>统计规律性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9fbqptqbs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,698,-4589.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 328 0 L 328 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 320 0 C 320 0 328 0 328 8 L 328 23 C 328 23 328 31 320 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 328 -4 C 328 -4 332 -4 332 0 L 332 31 C 332 31 332 35 328 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="308" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象有其偶然性的一面，也有其必然性的一面</p></div></foreignObject></g><g data-node-id="cr9fc5ewv4o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,698,-4548.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 384 0 L 384 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 376 0 C 376 0 384 0 384 8 L 384 23 C 384 23 384 31 376 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 384 -4 C 384 -4 388 -4 388 0 L 388 31 C 388 31 388 35 384 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="364" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>这种必然性表现为大量试验中随机事件出现的频率的稳定性</p></div></foreignObject></g><g data-node-id="cr9fciwd5mg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1112,-4570)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 356 0 L 356 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 348 0 C 348 0 356 0 356 8 L 356 23 C 356 23 356 31 348 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 356 -4 C 356 -4 360 -4 360 0 L 360 31 C 360 31 360 35 356 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="336" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一个随机事件出现的频率常在某个固定的常数附近摆动</p></div></foreignObject></g><g data-node-id="criwad3cl3c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-4257.1)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>排列组合</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwbefkue80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-4494.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>乘法原理</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwhyxd0c00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,800,-4507.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">n_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>种方法，进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">A_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">n_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>种方法，则进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程后接着进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">A_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程共有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mn>1</mn></msub><mo>×</mo><msub><mi>n</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">n_1 \times n_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>种方法</p></div></foreignObject></g><g data-node-id="criwbhc25tk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-4426.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>加法原理</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwizucsbc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,800,-4439.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">n_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>种方法，进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">A_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">n_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>种方法，假定<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程与<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">A_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>过程是并行的，则进行过程<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>或过程<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">A_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>的方法有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>n</mi><mn>1</mn></msub><mo>+</mo><msub><mi>n</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">n_1+n_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>种</p></div></foreignObject></g><g data-node-id="criwbj9pzyw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-4261.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>排列</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crja6xxiaqo0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4371.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 454 0 L 454 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 446 0 C 446 0 454 0 454 8 L 454 23 C 454 23 454 31 446 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 454 -4 C 454 -4 458 -4 458 0 L 458 31 C 458 31 458 35 454 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="434" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>从n个不同元素中任意选出r个元素排成一列，既考虑元素，也考虑顺序</p></div></foreignObject></g><g data-node-id="crja7oigae80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4328.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>重复排列数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crja8mnknh40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-4330.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 37 0 L 37 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 29 0 C 29 0 37 0 37 8 L 37 28 C 37 28 37 36 29 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 37 -4 C 37 -4 41 -4 41 0 L 41 36 C 41 36 41 40 37 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="17" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>n</mi><mi>r</mi></msup></mrow><annotation encoding="application/x-tex">n^r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6644em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crja7qyblio0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4250.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>选排列数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crja8qnjrh40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,888,-4284.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 318 0 L 318 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 310 0 C 310 0 318 0 318 8 L 318 45 C 318 45 318 53 310 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 318 -4 C 318 -4 322 -4 322 0 L 322 53 C 322 53 322 57 318 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="298" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>A</mi><mi>n</mi><mi>r</mi></msubsup><mo>=</mo><mi>n</mi><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>…</mo><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>n</mi><mo stretchy="false">!</mo></mrow><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mi>r</mi><mo stretchy="false">)</mo><mo stretchy="false">!</mo></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">A_n^r = n(n-1) \dots (n-r+1) = \dfrac{n!}{(n-r)!}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9303em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.453em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.3074em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">)!</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="mclose">!</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crjaam0ea340" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,888,-4221.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 121 0 L 121 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 113 0 C 113 0 121 0 121 8 L 121 28 C 121 28 121 36 113 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 121 -4 C 121 -4 125 -4 125 0 L 125 36 C 125 36 125 40 121 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="101" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>A</mi><mi>n</mi><mi>r</mi></msubsup><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mi>r</mi><mo>&gt;</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">A_n^r = 0,r &gt; n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9303em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.453em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crja7tc45k00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4151.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>全排列</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crja91efz940" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,874,-4175.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 78 0 L 78 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 70 0 C 70 0 78 0 78 8 L 78 28 C 78 28 78 36 70 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 78 -4 C 78 -4 82 -4 82 0 L 82 36 C 82 36 82 40 78 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="58" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mi>n</mi></msub><mo>=</mo><mi>n</mi><mo stretchy="false">!</mo></mrow><annotation encoding="application/x-tex">P_n = n!</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">n</span><span class="mclose">!</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crjaai7jktc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,874,-4129.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 64 0 L 64 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 56 0 C 56 0 64 0 64 8 L 64 26 C 64 26 64 34 56 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 64 -4 C 64 -4 68 -4 68 0 L 68 34 C 68 34 68 38 64 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="44" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo stretchy="false">!</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">0!=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">0</span><span class="mclose">!</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwbwveq400" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,684,-4019.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>组合</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crja800t38g0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4085.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 398 0 L 398 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 390 0 C 390 0 398 0 398 8 L 398 23 C 398 23 398 31 390 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 398 -4 C 398 -4 402 -4 402 0 L 402 31 C 402 31 402 35 398 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="378" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>从n个不同元素中任意选出r个元素，只考虑元素，不考虑顺序</p></div></foreignObject></g><g data-node-id="crja8i42we80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-4042.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>重复组合数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crjad4k1fm80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,902,-4044.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 119 0 L 119 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 111 0 C 111 0 119 0 119 8 L 119 28 C 119 28 119 36 111 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 119 -4 C 119 -4 123 -4 123 0 L 123 36 C 123 36 123 40 119 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="99" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>H</mi><mi>n</mi><mi>r</mi></msubsup><mo>=</mo><mrow><mo fence="true">(</mo><mfrac linethickness="0px"><mrow><mi>n</mi><mo>+</mo><mi>r</mi><mo>−</mo><mn>1</mn></mrow><mi>r</mi></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">H_n^r = \binom{n+r-1}{r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9303em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.453em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2451em;vertical-align:-0.35em;"></span><span class="mord"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8951em;"><span style="top:-2.355em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.144em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crja8ga9esg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,772,-3954.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>组合数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crjabzf6vk00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,874,-3998.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 37.5 L 0 0 L 356 0 L 356 75 L 0 75 L 0 37.5 Z"/><path d="M 0 37.5 L 0 8 C 0 8 0 0 8 0 L 348 0 C 348 0 356 0 356 8 L 356 67 C 356 67 356 75 348 75 L 8 75 C 8 75 0 75 0 67 L 0 37.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 37.5 L -4 0 C -4 0 -4 -4 0 -4 L 356 -4 C 356 -4 360 -4 360 0 L 360 75 C 360 75 360 79 356 79 L 0 79 C 0 79 -4 79 -4 75 L -4 37.5 Z" fill="none"/><foreignObject width="336" height="61" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">(</mo><mfrac linethickness="0px"><mi>n</mi><mi>r</mi></mfrac><mo fence="true">)</mo></mrow><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>n</mi><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>…</mo><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow><mi>r</mi><mo stretchy="false">!</mo></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mn>1</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mi>n</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mi>r</mi><mo>&gt;</mo><mi>n</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">\binom{n}{r} = \begin{cases}

\dfrac{n(n-1) \dots (n-r+1)}{r!} &amp;, 1 \leq r \leq n \\

0 &amp;, r &gt; n

\end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="mord"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7454em;"><span style="top:-2.355em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.144em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3.6em;vertical-align:-1.55em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em;"><span style="top:-2.5em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.492em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.016em" style="width:0.8889em" viewBox="0 0 888.89 16" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"/></svg></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.016em" style="width:0.8889em" viewBox="0 0 888.89 16" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"/></svg></span></span><span style="top:-4.3em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0265em;"><span style="top:-4.0265em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">!</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.3325em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5265em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0265em;"><span style="top:-4.0265em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">n</span></span></span><span style="top:-2.3325em;"><span class="pstrut" style="height:3.427em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5265em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="crjacwy2t7c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,874,-3913.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 74 0 L 74 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 66 0 C 66 0 74 0 74 8 L 74 27 C 74 27 74 35 66 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C -4 0 -4 -4 0 -4 L 74 -4 C 74 -4 78 -4 78 0 L 78 35 C 78 35 78 39 74 39 L 0 39 C 0 39 -4 39 -4 35 L -4 17.5 Z" fill="none"/><foreignObject width="54" height="21" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">(</mo><mfrac linethickness="0px"><mi>n</mi><mn>0</mn></mfrac><mo fence="true">)</mo></mrow><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\binom{n}{0} = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="mord"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7454em;"><span style="top:-2.355em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span><span style="top:-3.144em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwvftfshk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,568,-3448.1)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>确定概率的方法</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cr9erulosxc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,726,-3743.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>古典概型</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criw4feup080" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3834.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>基本思想</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criw2oypjps0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-3868.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 520 0 L 520 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 45 C 520 45 520 53 512 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 53 C 524 53 524 57 520 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="500" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象的全部可能结果只有有限个，譬如n个，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>ω</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>ω</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\omega_1, \omega_2, \dots, \omega_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>，这些事件两两互不相容</p></div></foreignObject></g><g data-node-id="criw3lsv55c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-3805.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 471 0 L 471 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 463 0 C 463 0 471 0 471 8 L 471 28 C 471 28 471 36 463 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 471 -4 C 471 -4 475 -4 475 0 L 475 36 C 475 36 475 40 471 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="451" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ω</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>ω</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>ω</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\omega_1, \omega_2, \dots, \omega_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>的发生或出现是等可能的，即它们发生的概率都一样</p></div></foreignObject></g><g data-node-id="criw8vhqcn40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3750.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率的古典定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criw8xmpwp40" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1000,-3759.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24.5 L 0 0 L 251 0 L 251 49 L 0 49 L 0 24.5 Z"/><path d="M 0 24.5 L 0 8 C 0 8 0 0 8 0 L 243 0 C 243 0 251 0 251 8 L 251 41 C 251 41 251 49 243 49 L 8 49 C 8 49 0 49 0 41 L 0 24.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24.5 L -4 0 C -4 0 -4 -4 0 -4 L 251 -4 C 251 -4 255 -4 255 0 L 255 49 C 255 49 255 53 251 53 L 0 53 C 0 53 -4 53 -4 49 L -4 24.5 Z" fill="none"/><foreignObject width="231" height="35" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mi>m</mi><mi>n</mi></mfrac></mstyle><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>A</mi><mtext>的有利场合的数目</mtext></mrow><mtext>样本点总数</mtext></mfrac></mstyle></mrow><annotation encoding="application/x-tex">P=\dfrac{m}{n}=\dfrac{A的有利场合的数目}{样本点总数}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.7936em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord cjk_fallback">样本点总数</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord cjk_fallback">的有利场合的数目</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwcs54ypk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3652.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 174 0 L 174 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 166 0 C 166 0 174 0 174 8 L 174 23 C 174 23 174 31 166 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 174 -4 C 174 -4 178 -4 178 0 L 178 31 C 178 31 178 35 174 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="154" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>古典概型概率的基本性质</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,183,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwgbnh09s0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1056,-3700.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 198 0 L 198 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 190 0 C 190 0 198 0 198 8 L 198 28 C 198 28 198 36 190 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 198 -4 C 198 -4 202 -4 202 0 L 202 36 C 202 36 202 40 198 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="178" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于任何事件A，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(A) \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwgknp0m80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1056,-3654.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 90 0 L 90 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 28 C 90 28 90 36 82 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 36 C 94 36 94 40 90 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="70" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\Omega)=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">Ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwgnzxkm80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1056,-3608.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 689 0 L 689 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 681 0 C 681 0 689 0 689 8 L 689 28 C 689 28 689 36 681 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 689 -4 C 689 -4 693 -4 693 0 L 693 36 C 693 36 693 40 689 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="669" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="669px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 669px; max-width: 669px;"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>A</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>A</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">A_1, A_2,\dots,A_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>两两互不相容，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo>+</mo><msub><mi>A</mi><mn>2</mn></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mi>A</mi><mi>m</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo>+</mo><mo>⋯</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>m</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_1+A_2+\dots+A_m)=P(A_1)+P(A_2)+\dots+P(A_m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cr9ery9umsg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,726,-3442.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>几何概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwlq8q62g0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3532.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>基本思想</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwmx5w2so0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-3562.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 354 0 L 354 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 346 0 C 346 0 354 0 354 8 L 354 26 C 354 26 354 34 346 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 354 -4 C 354 -4 358 -4 358 0 L 358 34 C 358 34 358 38 354 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="334" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机现象的样本空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>充满整个区域，存在无限多结果</p></div></foreignObject></g><g data-node-id="criwnqgtj0o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-3518.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>落在某区域g的概率与区域的测度（长度、面积或体积等）成正比并且与其位置及形状无关</p></div></foreignObject></g><g data-node-id="criwove4lbc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3451.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率的几何定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwoxh49lc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1000,-3460.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24.5 L 0 0 L 157 0 L 157 49 L 0 49 L 0 24.5 Z"/><path d="M 0 24.5 L 0 8 C 0 8 0 0 8 0 L 149 0 C 149 0 157 0 157 8 L 157 41 C 157 41 157 49 149 49 L 8 49 C 8 49 0 49 0 41 L 0 24.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24.5 L -4 0 C -4 0 -4 -4 0 -4 L 157 -4 C 157 -4 161 -4 161 0 L 161 49 C 161 49 161 53 157 53 L 0 53 C 0 53 -4 53 -4 49 L -4 24.5 Z" fill="none"/><foreignObject width="137" height="35" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>g</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>g</mi><mtext>的测度</mtext></mrow><mrow><mi mathvariant="normal">Ω</mi><mtext>的测度</mtext></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">P(A_g) = \dfrac{g的测度}{\Omega的测度}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">Ω</span><span class="mord cjk_fallback">的测度</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord cjk_fallback">的测度</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwqag25xk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3353.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>几何概率的基本性质</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,155,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwrokqtfk0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1028,-3401.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 198 0 L 198 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 190 0 C 190 0 198 0 198 8 L 198 28 C 198 28 198 36 190 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 198 -4 C 198 -4 202 -4 202 0 L 202 36 C 202 36 202 40 198 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="178" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于任何事件A，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(A) \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwrokqp280" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1028,-3355.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 90 0 L 90 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 28 C 90 28 90 36 82 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 36 C 94 36 94 40 90 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="70" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\Omega)=1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">Ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwrokqq4o0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1028,-3309.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 463 0 L 463 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 455 0 C 455 0 463 0 463 8 L 463 28 C 463 28 463 36 455 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 463 -4 C 463 -4 467 -4 467 0 L 467 36 C 467 36 467 40 463 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="443" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>A</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>A</mi><mi>m</mi></msub></mrow><annotation encoding="application/x-tex">A_1, A_2,\dots,A_m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>两两互不相容，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msubsup><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\sum_{n=1}^{\infty} A_n)=\sum_{n=1}^{\infty} P(A_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="criwvliafm00" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,726,-3152.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>主观概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwzdgen140" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3255.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>基本思想</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwvykifds0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,958,-3263.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一个事件的概率是人们根据经验对该事件发生的可能性所给出的个人信念，这样给出的概率称为主观概率</p></div></foreignObject></g><g data-node-id="criwzj9hi4g0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,842,-3050.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>注意</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwyzer1ns0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-3168.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 258 0 L 258 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 250 0 C 250 0 258 0 258 8 L 258 23 C 258 23 258 31 250 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 258 -4 C 258 -4 262 -4 262 0 L 262 31 C 262 31 262 35 258 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="238" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>主观概率和主观臆造有着本质上的不同</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,267,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwyzeql0w0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1228,-3205.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>前者要求当事人对所考察的事件有透彻的了解和丰富的经验，甚至是这一行的专家，并能对历史信息和当时信息进行仔细分析</p></div></foreignObject></g><g data-node-id="criwzqea69c0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1228,-3147.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>如此确定的主观概率是可信的，从某种意义上说，不利用这些丰富的经验也是一种浪费</p></div></foreignObject></g><g data-node-id="criwyzeriig0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-3081.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 300 0 L 300 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 292 0 C 292 0 300 0 300 8 L 300 23 C 300 23 300 31 292 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 300 -4 C 300 -4 304 -4 304 0 L 304 31 C 304 31 304 35 300 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="280" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>用主观方法得出的随机事件发生的可能性大小</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,309,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwyzerfko0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1270,-3089.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>本质上是对随机事件概率的一种推断和估计，虽然结论的精确性有待实践的检验和修正，但结论的可信性在统计意义上是有其价值的</p></div></foreignObject></g><g data-node-id="criwyzerkkw0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-3031.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 468 0 L 468 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 460 0 C 460 0 468 0 468 8 L 468 23 C 468 23 468 31 460 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 468 -4 C 468 -4 472 -4 472 0 L 472 31 C 472 31 472 35 468 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="448" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在遇到的随机现象无法大量重复时，用主观方法去做决策和判断是适合的</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,477,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="criwz5tboe80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1438,-3031.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 314 0 L 314 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 306 0 C 306 0 314 0 314 8 L 314 23 C 314 23 314 31 306 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 314 -4 C 314 -4 318 -4 318 0 L 318 31 C 318 31 318 35 314 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="294" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>从这点看，主观方法至少是频率方法的一种补充</p></div></foreignObject></g><g data-node-id="criwyzer9880" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-2990.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>另外要说明的是，主观概率的确定除根据自己的经验外，决策者还可以利用别人的经验</p></div></foreignObject></g><g data-node-id="criwyzerrfs0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,930,-2932.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 244 0 L 244 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 236 0 C 236 0 244 0 244 8 L 244 23 C 244 23 244 31 236 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 244 -4 C 244 -4 248 -4 248 0 L 248 31 C 248 31 248 35 244 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="224" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>主观给定的概率要符合公理化的定义</p></div></foreignObject></g><g data-node-id="crig560egcg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1966,-5238)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>频率稳定于概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="crig5dos8yg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2124,-5261)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 288 0 L 288 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 280 0 C 280 0 288 0 288 8 L 288 28 C 288 28 288 36 280 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 288 -4 C 288 -4 292 -4 292 0 L 292 36 C 292 36 292 40 288 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="268" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>当N足够大时，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mi>N</mi></msub><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F_N(A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span></span></span></span></span>与<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span></span></span></span></span>应充分接近</p></div></foreignObject></g><g data-node-id="crig5dosp280" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2124,-5215)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 311 0 L 311 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 303 0 C 303 0 311 0 311 8 L 311 23 C 311 23 311 31 303 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 311 -4 C 311 -4 315 -4 315 0 L 315 31 C 315 31 315 35 311 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="291" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>当N足够大时，用它的频率来作为概率的近似值</p></div></foreignObject></g><g data-node-id="crih0zrp9a80" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2090,-5724)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 169 0 L 169 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 161 0 C 161 0 169 0 169 8 L 169 29 C 169 29 169 37 161 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 169 -4 C 169 -4 173 -4 173 0 L 173 37 C 173 37 173 41 169 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="149" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo separator="true">,</mo><mi mathvariant="script">F</mi><mo separator="true">,</mo><mi>P</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\Omega,\mathscr{F},P)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">Ω</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mclose">)</span></span></span></span></span><strong>称为概率空间</strong></p></div></foreignObject></g><g data-node-id="GMfhCRrlRQvxYmJCr9wPT" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,658,-2667.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>条件概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="_qaqMwAXQAVbPTXEacfe4" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,774,-2838.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="6NoIeieEF35LrWvx91p_-" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,862,-2861.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 38.5 L 0 0 L 520 0 L 520 77 L 0 77 L 0 38.5 Z"/><path d="M 0 38.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 69 C 520 69 520 77 512 77 L 8 77 C 8 77 0 77 0 69 L 0 38.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 38.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 77 C 524 77 524 81 520 81 L 0 81 C 0 81 -4 81 -4 77 L -4 38.5 Z" fill="none"/><foreignObject width="500" height="63" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>设<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo separator="true">,</mo><mi mathvariant="script">F</mi><mo separator="true">,</mo><mi>P</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\Omega, \mathscr{F}, P)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">Ω</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mclose">)</span></span></span></span></span>是一个概率空间，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">B \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>，而且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(B)&gt;0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，则对任意<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">A \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span>，记<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo></mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">P(A|B) = \dfrac{P(AB)}{P(B)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>为在事件B发生的条件下事件A发生的条件概率</p></div></foreignObject></g><g data-node-id="6yRBdtEpuiPw5AlYYxdbe" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,774,-2749.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>乘法公式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="PTkJxCLEZ2w1_j66Kh-xw" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,890,-2774.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 312 0 L 312 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 304 0 C 304 0 312 0 312 8 L 312 28 C 312 28 312 36 304 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 312 -4 C 312 -4 316 -4 316 0 L 316 36 C 316 36 316 40 312 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="292" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi mathvariant="normal">∣</mi><mi>A</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(AB) = P(B)P(A|B) = P(A)P(B|A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord">∣</span><span class="mord mathnormal">A</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="mooq6pTDHkpEd5_5_CrdP" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,890,-2728.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 555 0 L 555 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 547 0 C 547 0 555 0 555 8 L 555 28 C 555 28 555 36 547 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 555 -4 C 555 -4 559 -4 559 0 L 559 36 C 559 36 559 40 555 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="535" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="535px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 535px; max-width: 535px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>A</mi><mn>2</mn></msub><mo>…</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>2</mn></msub><mi mathvariant="normal">∣</mi><msub><mi>A</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>3</mn></msub><mi mathvariant="normal">∣</mi><msub><mi>A</mi><mn>1</mn></msub><msub><mi>A</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo>…</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>n</mi></msub><mi mathvariant="normal">∣</mi><msub><mi>A</mi><mn>1</mn></msub><msub><mi>A</mi><mn>2</mn></msub><mo>…</mo><msub><mi>A</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_1A_2 \dots A_n) = P(A_1)P(A_2|A_1)P(A_3|A_1A_2) \dots P(A_n|A_1A_2 \dots A_{n-1})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="9avXgMkK-oYDQb4wnrcXC" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,774,-2634.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 258 0 L 258 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 250 0 C 250 0 258 0 258 8 L 258 23 C 258 23 258 31 250 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 258 -4 C 258 -4 262 -4 262 0 L 262 31 C 262 31 262 35 258 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="238" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>条件概率是概率，满足概率公理化体系</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,267,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="yG2FGo_VnusXSVgdZqiZy" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1072,-2636.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 105 0 L 105 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 97 0 C 97 0 105 0 105 8 L 105 28 C 105 28 105 36 97 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 105 -4 C 105 -4 109 -4 109 0 L 109 36 C 109 36 109 40 105 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="85" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>设<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(B)&gt;0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,114,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="TcHpgf1f09hiOBxmxLaen" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1217,-2680.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>非负性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="g-nIfERTEQxbrFVWkEoGh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1319,-2682.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 109 0 L 109 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 101 0 C 101 0 109 0 109 8 L 109 28 C 109 28 109 36 101 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 109 -4 C 109 -4 113 -4 113 0 L 113 36 C 113 36 113 40 109 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="89" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(A|B) \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="3XjhCH2PuzOizEYLfeYYG" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1217,-2634.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>正则性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="YH7C8iaWaoSjNqaXQuZ1M" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1319,-2636.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 108 0 L 108 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 100 0 C 100 0 108 0 108 8 L 108 28 C 108 28 108 36 100 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 108 -4 C 108 -4 112 -4 112 0 L 112 36 C 112 36 112 40 108 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="88" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\Omega | B) = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">Ω∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="32uPeVAu0ieGbIAKkOM6Y" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1217,-2588.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>可列可加性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Qh3QYONV7rWEwRyYKqoeg" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1347,-2590.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 254 0 L 254 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 246 0 C 246 0 254 0 254 8 L 254 28 C 254 28 254 36 246 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 254 -4 C 254 -4 258 -4 258 0 L 258 36 C 258 36 258 40 254 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="234" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\sum_{i=1}^{\infty} A_i | B) = \sum_{i=1}^{\infty} P(A_i |B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="whD4OA-SP1iyb7olMWoRB" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,774,-2496.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>条件概率其他性质</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="mxTachDqUD2LkOL44HrLF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,946,-2544.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 104 0 L 104 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 28 C 104 28 104 36 96 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 36 C 108 36 108 40 104 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="84" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">∅</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(\emptyset | B) = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord">∅∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="hjfkJezNPd1zLqVK9ggS2" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,946,-2498.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 187 0 L 187 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 179 0 C 179 0 187 0 187 8 L 187 28 C 187 28 187 36 179 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 187 -4 C 187 -4 191 -4 191 0 L 191 36 C 191 36 191 40 187 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="167" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>P</mi><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A|B) = 1 - P(\overline{A} | B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1333em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="mTnf0S9CDQk6wo9AJbwAh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,946,-2452.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 404 0 L 404 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 396 0 C 396 0 404 0 404 8 L 404 28 C 404 28 404 36 396 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 404 -4 C 404 -4 408 -4 408 0 L 408 36 C 408 36 408 40 404 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="384" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mo>∪</mo><msub><mi>A</mi><mn>2</mn></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>2</mn></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>−</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>A</mi><mn>2</mn></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_1 \cup A_2 | B) = P(A_1|B) + P(A_2|B) - P(A_1A_2 | B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∪</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="lAuhgK0rHj_ScCQcuY8xX" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,658,-2365.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>全概率公式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="lyLDCTdBhliYkdkH-Lv9I" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-2393.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Li_XkD_XfYQv3Nh3QLjjF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,876,-2395.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 446 0 L 446 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 438 0 C 438 0 446 0 446 8 L 446 28 C 446 28 446 36 438 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 446 -4 C 446 -4 450 -4 450 0 L 450 36 C 450 36 450 40 446 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="426" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi mathvariant="normal">∣</mi><mi>A</mi><mo stretchy="false">)</mo><mo>+</mo><mi>P</mi><mo stretchy="false">(</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi mathvariant="normal">∣</mi><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(B) = P(AB) + P(\overline{A}B) = P(A)P(B|A) + P(\overline{A})P(B|\overline{A})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1333em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord">∣</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1333em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord">∣</span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,455,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="4kAbMSglyG1IlBkHkQtH8" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1362,-2406.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 548 0 L 548 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 540 0 C 540 0 548 0 548 8 L 548 50 C 548 50 548 58 540 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 548 -4 C 548 -4 552 -4 552 0 L 552 58 C 552 58 552 62 548 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="528" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="528px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 528px; max-width: 528px;"><p>设事件<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>A</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>A</mi><mi>n</mi></msub><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">A_1,A_2,\dots,A_n,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>是样本空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>的一个分割，亦称完备事件组，即<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi><mo separator="true">,</mo><mo>…</mo><mtext> </mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">A_i(i=1,2,\dots,n,\dots)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mclose">)</span></span></span></span></span>两两互不相容，而且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub><mo>=</mo><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\sum_{i=1}^{\infty} A_i = \Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>，则有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msub><mi>A</mi><mi>i</mi></msub><mi>B</mi></mrow><annotation encoding="application/x-tex">B = \sum_{i=1}^{\infty} A_iB</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,557,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="2ceXEde2dBJOJUuaUUMXq" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1950,-2395.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 183 0 L 183 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 175 0 C 175 0 183 0 183 8 L 183 28 C 183 28 183 36 175 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 183 -4 C 183 -4 187 -4 187 0 L 187 36 C 187 36 187 40 183 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="163" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(B) = \sum_{i=1}^{\infty} P(A_iB)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,192,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="8B_0QW7yhwxcPi7VP79L1" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2173,-2395.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 233 0 L 233 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 225 0 C 225 0 233 0 233 8 L 233 28 C 233 28 233 36 225 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 233 -4 C 233 -4 237 -4 237 0 L 237 36 C 237 36 237 40 233 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="213" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi mathvariant="normal">∣</mi><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(B) = \sum_{i=1}^{\infty} P(A_i) P(B|A_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="krHXphAsCG5_22dpMk8D7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-2338.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 202 0 L 202 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 194 0 C 194 0 202 0 202 8 L 202 23 C 202 23 202 31 194 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 202 -4 C 202 -4 206 -4 206 0 L 206 31 C 206 31 206 35 202 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="182" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率论中使用频率最高的公式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,211,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="wODnC6smoUjSfR29CUjBt" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1030,-2338.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>逐个击破，分而食之</p></div></foreignObject></g><g data-node-id="w4Zs6RCpVA4923ZtZwSHI" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,658,-2193.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>贝叶斯公式</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="IgcXh-i1NKAMSSRGU9r7D" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-2284.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="pIti-1tab0YAb8fkyAQru" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,876,-2297.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若事件B能且只能与两两互不相容的事件<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>A</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>A</mi><mi>n</mi></msub><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">A_1,A_2,\dots,A_n,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>之一同时发生，即<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>B</mi><msub><mi>A</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">B = \sum_{i=1}^{\infty} BA_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="NMNt95q8K6A0heHtzQ33F" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1436,-2296.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 27.5 L 0 0 L 263 0 L 263 55 L 0 55 L 0 27.5 Z"/><path d="M 0 27.5 L 0 8 C 0 8 0 0 8 0 L 255 0 C 255 0 263 0 263 8 L 263 47 C 263 47 263 55 255 55 L 8 55 C 8 55 0 55 0 47 L 0 27.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 27.5 L -4 0 C -4 0 -4 -4 0 -4 L 263 -4 C 263 -4 267 -4 267 0 L 267 55 C 267 55 267 59 263 59 L 0 59 C 0 59 -4 59 -4 55 L -4 27.5 Z" fill="none"/><foreignObject width="243" height="41" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi mathvariant="normal">∣</mi><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi mathvariant="normal">∣</mi><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">P(A_i|B) = \dfrac{P(A_i)P(B|A_i)}{\sum_{i=1}^{\infty} P(A_j) P(B|A_j)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.421em;vertical-align:-0.994em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.3057em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord">∣</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="rQcD05hD4Nu3QPPXxrHXZ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-2198.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>先验概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="SBVTA2QbbuVExmcwtyK2r" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,904,-2229.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 65 0 L 65 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 57 0 C 57 0 65 0 65 8 L 65 28 C 65 28 65 36 57 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 65 -4 C 65 -4 69 -4 69 0 L 69 36 C 69 36 69 40 65 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="45" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="nIlPEshEJ5p6ppBAsALgH" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,904,-2183.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>反映“各种”原因发生的可能性大小，一般是以往经验的总结，在这次实验前已经知道</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,24)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Sr03ywO8YWilmLhNr1-Lb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1464,-2175.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 216 0 L 216 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 208 0 C 208 0 216 0 216 8 L 216 23 C 216 23 216 31 208 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 216 -4 C 216 -4 220 -4 220 0 L 220 31 C 220 31 220 35 216 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="196" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>有助于探讨事件发生的“原因”</p></div></foreignObject></g><g data-node-id="B4gFPgScYUDjjBmo-ukAH" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-2102.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>后验概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="PVc0j-9Nl8KKjKdzzDF9q" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,904,-2125.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 84 0 L 84 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 76 0 C 76 0 84 0 84 8 L 84 28 C 84 28 84 36 76 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 84 -4 C 84 -4 88 -4 88 0 L 88 36 C 88 36 88 40 84 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="64" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_i|B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="6o0D1NLgYOEtj7yDPHsP7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,904,-2079.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 384 0 L 384 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 376 0 C 376 0 384 0 384 8 L 384 23 C 384 23 384 31 376 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 384 -4 C 384 -4 388 -4 388 0 L 388 31 C 388 31 388 35 384 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="364" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>反映了实验之后对各种“原因”发生的可能性大小的新知识</p></div></foreignObject></g><g data-node-id="KmzCDAE-eDmnvxmbwvPCp" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1710,-2155)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 272 0 L 272 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 264 0 C 264 0 272 0 272 8 L 272 23 C 272 23 272 31 264 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 272 -4 C 272 -4 276 -4 276 0 L 276 31 C 276 31 276 35 272 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="252" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>后验概率的大小很受先验概率选取的影响</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,281,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="a8pooFHG9y_F04kMEXfYY" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2022,-2155)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 370 0 L 370 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 362 0 C 362 0 370 0 370 8 L 370 23 C 370 23 370 31 362 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 370 -4 C 370 -4 374 -4 374 0 L 374 31 C 374 31 374 35 370 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="350" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>先验概率的选取也成为贝叶斯公式使用中最有争议的地方</p></div></foreignObject></g><g data-node-id="xMGMCJ2ZAekM2Ge3KOs2K" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,658,-1513.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>统计独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="BoTn6DRJGS-ogfFtAZPyL" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-1737.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="b1E_pAcipz6C7WeFrpydS" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-2002.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>两个事件的独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="3_4Pt-PUHh3heZzA45aYb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1090,-2036.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="BlVAG0y24hyLTp-BnjwET" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1178,-2038.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 501 0 L 501 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 493 0 C 493 0 501 0 501 8 L 501 28 C 501 28 501 36 493 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 501 -4 C 501 -4 505 -4 505 0 L 505 36 C 505 36 505 40 501 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="481" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对事件A及B，若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(AB) = P(A)P(B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span>则称它们是统计独立的，简称独立的</p></div></foreignObject></g><g data-node-id="A1oDc38K3GDIQPZETigRE" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1090,-1968.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>推论</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="6EoMIs347oPlqaEGlkYxT" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1178,-1992.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 369 0 L 369 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 361 0 C 361 0 369 0 369 8 L 369 28 C 369 28 369 36 361 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 369 -4 C 369 -4 373 -4 373 0 L 373 36 C 373 36 373 40 369 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="349" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若事件A与B独立，且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(B) &gt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi mathvariant="normal">∣</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A|B) = P(A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,378,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="7GJXmGwEvZM5xHtyhVYWW" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1587,-1990.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 571 0 L 571 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 563 0 C 563 0 571 0 571 8 L 571 23 C 571 23 571 31 563 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 571 -4 C 571 -4 575 -4 575 0 L 575 31 C 575 31 575 35 571 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="551" height="17" x="0" y="0" class="text-obj" maxwidth="551px" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 551px; max-width: 551px;"><p>事件B发生与否，对事件A发生的概率没有影响，亦即B的发生没有对A提供任何的信息</p></div></foreignObject></g><g data-node-id="JsS2EZpmP_JJs5vLCadr2" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1178,-1944.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 305 0 L 305 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 297 0 C 297 0 305 0 305 8 L 305 23 C 305 23 305 31 297 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 305 -4 C 305 -4 309 -4 309 0 L 309 31 C 309 31 309 35 305 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="285" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若事件A与B独立，则下列各对事件也相互独立</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,314,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="w7e3wMLCcGctUXhd7OG-6" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1523,-1946.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 197 0 L 197 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 189 0 C 189 0 197 0 197 8 L 197 28 C 197 28 197 36 189 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 197 -4 C 197 -4 201 -4 201 0 L 201 36 C 201 36 201 40 197 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="177" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">{</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">,</mo><mi>B</mi><mo fence="true">}</mo></mrow><mtext> </mtext><mrow><mo fence="true">{</mo><mi>A</mi><mo separator="true">,</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo fence="true">}</mo></mrow><mtext> </mtext><mrow><mo fence="true">{</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">,</mo><mover accent="true"><mi>B</mi><mo stretchy="true">‾</mo></mover><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">\left\{ \overline{A}, B \right\}~\left\{ A, \overline{B} \right\}~\left\{ \overline{A}, \overline{B} \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2333em;vertical-align:-0.35em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">{</span></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">}</span></span></span><span class="mspace nobreak"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">{</span></span><span class="mord mathnormal">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">}</span></span></span><span class="mspace nobreak"> </span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">{</span></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">}</span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="HBu7fBCrSRyQuh09xqJyh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1829.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>三个事件的独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="clhEIDN39Zk7IcX-M_7OE" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1090,-1829.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 454 0 L 454 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 446 0 C 446 0 454 0 454 8 L 454 23 C 454 23 454 31 446 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 454 -4 C 454 -4 458 -4 458 0 L 458 31 C 458 31 458 35 454 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="434" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于三个事件A，B，C，若下列四个等式同时成立，则称它们相互独立</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,463,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="pYzfG440Nt6YN0XBkecKr" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1584,-1900.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 175 0 L 175 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 167 0 C 167 0 175 0 175 8 L 175 28 C 175 28 175 36 167 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 175 -4 C 175 -4 179 -4 179 0 L 179 36 C 179 36 179 40 175 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="155" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(AB) = P(A)P(B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="6Quz4lZbHcnqTNe1uwklf" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1584,-1854.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 175 0 L 175 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 167 0 C 167 0 175 0 175 8 L 175 28 C 175 28 175 36 167 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 175 -4 C 175 -4 179 -4 179 0 L 179 36 C 179 36 179 40 175 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="155" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mi>C</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(BC) = P(B)P(C)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="IErQqtKMHdh23wAvyRVnx" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1584,-1808.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 174 0 L 174 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 166 0 C 166 0 174 0 174 8 L 174 28 C 174 28 174 36 166 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 174 -4 C 174 -4 178 -4 178 0 L 178 36 C 178 36 178 40 174 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="154" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>C</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(AC) = P(A)P(C)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="97sVpalsnr2HxY0fztP0o" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1584,-1762.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 227 0 L 227 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 219 0 C 219 0 227 0 227 8 L 227 28 C 227 28 227 36 219 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 227 -4 C 227 -4 231 -4 231 0 L 231 36 C 231 36 231 40 227 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="207" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mi>B</mi><mi>C</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(ABC) = P(A)P(B)P(C)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,236,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="5EZitnHq7_-335lkUBDzo" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1841,-1761)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>三者独立</p></div></foreignObject></g><g data-node-id="YZjakVzl7VbM_LHQxjjde" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1789,-1853)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 80 0 L 80 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 72 0 C 72 0 80 0 80 8 L 80 23 C 80 23 80 31 72 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 80 -4 C 80 -4 84 -4 84 0 L 84 31 C 84 31 84 35 80 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="60" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p> 两两独立</p></div></foreignObject></g><g data-node-id="GJ6gDXV4X2TkV3ILYwsW8" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1646.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>有限多个事件的独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="eEXhVqAAoRPYZPcSMaUiV" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1118,-1668.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 37.5 L 0 0 L 520 0 L 520 75 L 0 75 L 0 37.5 Z"/><path d="M 0 37.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 67 C 520 67 520 75 512 75 L 8 75 C 8 75 0 75 0 67 L 0 37.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 37.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 75 C 524 75 524 79 520 79 L 0 79 C 0 79 -4 79 -4 75 L -4 37.5 Z" fill="none"/><foreignObject width="500" height="61" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对n个事件<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>A</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>A</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">A_1,A_2,\dots,A_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>，若对于所有可能的组合<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>≤</mo><mi>i</mi><mo>&lt;</mo><mi>j</mi><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mo>⋯</mo><mo>≤</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">1 \leq i &lt; j &lt; k &lt; \dots \leq n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></span>，成立如下<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>C</mi><mi>n</mi><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>C</mi><mi>n</mi><mn>3</mn></msubsup><mo>+</mo><mo>⋯</mo><mo>+</mo><msubsup><mi>C</mi><mi>n</mi><mi>n</mi></msubsup><mo>=</mo><msup><mn>2</mn><mi>n</mi></msup><mo>−</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">C_n^2 + C_n^3 + \dots + C_n^n = 2^n - n- 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0611em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0611em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.9303em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7477em;vertical-align:-0.0833em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span>个等式，则称这n个事件相互独立</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,37.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="i5GrCdcK8XnYYTsPj09fF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1678,-1716.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 198 0 L 198 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 190 0 C 190 0 198 0 198 8 L 198 28 C 198 28 198 36 190 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 198 -4 C 198 -4 202 -4 202 0 L 202 36 C 202 36 202 40 198 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="178" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_iA_j) = P(A_i)P(A_j)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,207,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="oUWSb3IUteFu2X0JBqUCb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1916,-1714.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>两两独立</p></div></foreignObject></g><g data-node-id="QAH6zbnNH-gLOufbXsCw8" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1678,-1670.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 267 0 L 267 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 259 0 C 259 0 267 0 267 8 L 267 28 C 267 28 267 36 259 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 267 -4 C 267 -4 271 -4 271 0 L 271 36 C 271 36 271 40 267 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="247" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><msub><mi>A</mi><mi>j</mi></msub><msub><mi>A</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_iA_jA_k) = P(A_i)P(A_j)P(A_k)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,276,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="E8XiiD7ULUBXteSGNX2rL" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1985,-1668.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>三三独立</p></div></foreignObject></g><g data-node-id="b73obd9GUaLBuS-wdjR_V" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1678,-1624.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 40 0 L 40 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 32 0 C 32 0 40 0 40 8 L 40 26 C 40 26 40 34 32 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 40 -4 C 40 -4 44 -4 44 0 L 44 34 C 44 34 44 38 40 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="20" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>…</mo></mrow><annotation encoding="application/x-tex">\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.123em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="gEPEzgmhVjK2_X0RM2_fh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1678,-1580.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 318 0 L 318 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 310 0 C 310 0 318 0 318 8 L 318 28 C 318 28 318 36 310 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 318 -4 C 318 -4 322 -4 322 0 L 322 36 C 322 36 322 40 318 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="298" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><msub><mi>A</mi><mi>j</mi></msub><mo>…</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>j</mi></msub><mo stretchy="false">)</mo><mo>…</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A_iA_j\dots A_n) = P(A_i)P(A_j)\dots P(A_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,327,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="-3MvbhTiyYHSf0vUF2Ovh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2036,-1578.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 71 0 L 71 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 63 0 C 63 0 71 0 71 8 L 71 23 C 71 23 71 31 63 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 71 -4 C 71 -4 75 -4 75 0 L 75 31 C 75 31 75 35 71 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="51" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>n个独立</p></div></foreignObject></g><g data-node-id="ztIl0vu0Rhs8cK0ZCs3kw" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2137,-1647)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 340 0 L 340 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 332 0 C 332 0 340 0 340 8 L 340 23 C 340 23 340 31 332 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 340 -4 C 340 -4 344 -4 344 0 L 344 31 C 344 31 344 35 340 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="320" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p> n个事件相互独立，则其任意m个事件也必相互独立</p></div></foreignObject></g><g data-node-id="emL0oSUCEZHnMUROcltym" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1534.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>无穷多个事件的独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="uMLvSsRZwgD3OA4M3S527" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1118,-1534.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 426 0 L 426 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 418 0 C 418 0 426 0 426 8 L 426 23 C 426 23 426 31 418 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 426 -4 C 426 -4 430 -4 430 0 L 430 31 C 430 31 430 35 426 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="406" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件中有任意有限多个事件都相互独立，则无穷多个事件相互独立</p></div></foreignObject></g><g data-node-id="XGZP0028Htwbdm3ZUFVHv" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1473.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件独立性与概率计算</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="qXNxvm0E5yjwuuA6te1WZ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1118,-1473.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 300 0 L 300 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 292 0 C 292 0 300 0 300 8 L 300 23 C 300 23 300 31 292 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 300 -4 C 300 -4 304 -4 304 0 L 304 31 C 304 31 304 35 300 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="280" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件独立，则许多概率的计算就可以大为简化</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,309,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="fZu-MlrzBhcLSI2e45btD" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1458,-1493.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 286 0 L 286 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 278 0 C 278 0 286 0 286 8 L 286 23 C 286 23 286 31 278 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 286 -4 C 286 -4 290 -4 290 0 L 290 31 C 290 31 290 35 286 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="266" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>相互独立的事件至少发生其一的概率的计算</p></div></foreignObject></g><g data-node-id="Y_afvQ-Bd_T5YhbHwbaRM" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1458,-1452.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>可靠性理论中的应用</p></div></foreignObject></g><g data-node-id="gMGF5ucd61n8-iW0W_BMI" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,788,-1289.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>试验独立性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="-Z0zK_y7QbC26RFYN3wOc" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1398.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 202 0 L 202 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 194 0 C 194 0 202 0 202 8 L 202 23 C 202 23 202 31 194 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 202 -4 C 202 -4 206 -4 206 0 L 206 31 C 206 31 206 35 202 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="182" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>试验的公共的样本空间的定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,211,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Ilzf0SBcSHzTgPC31ZeJF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1160,-1411.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 881 0 L 881 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 873 0 C 873 0 881 0 881 8 L 881 50 C 881 50 881 58 873 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 881 -4 C 881 -4 885 -4 885 0 L 885 58 C 885 58 885 62 881 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="861" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="861px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 861px; max-width: 861px;"><p>试验<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">E_{i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>的样本空间是<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">Ω</mi><mi>i</mi></msub><mo>=</mo><mrow><mo fence="true">{</mo><msup><mi>ω</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">\Omega_i = \left\{ \omega^{(i)} \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.238em;vertical-align:-0.35em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">{</span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">}</span></span></span></span></span></span></span>，构造复合试验E，表示依次进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">E_{i}(i=1,2,\dots,n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></span>试验，其样本点为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi><mo>=</mo><mo stretchy="false">(</mo><msup><mi>ω</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msup><mo separator="true">,</mo><msup><mi>ω</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msup><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msup><mi>ω</mi><mrow><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\omega = (\omega^{(1)},\omega^{(2)},\dots,\omega^{(n)})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">2</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">n</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span>，这个样本空间为样本空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="normal">Ω</mi><mi>i</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\Omega_i(i=1,2,\dots,n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span></span>的乘积空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi><mo>=</mo><msub><mi mathvariant="normal">Ω</mi><mn>1</mn></msub><mo>×</mo><msub><mi mathvariant="normal">Ω</mi><mn>2</mn></msub><mo>×</mo><mo>⋯</mo><mo>×</mo><msub><mi mathvariant="normal">Ω</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\Omega = \Omega_1 \times \Omega_2 \times \dots \times \Omega_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord">Ω</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="PYT029LmFaN-ccr2CV-S4" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1340.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>试验独立性的定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="y_g0s7cxEepqKqnFYWBZZ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1090,-1343.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 1256 0 L 1256 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 1248 0 C 1248 0 1256 0 1256 8 L 1256 29 C 1256 29 1256 37 1248 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 1256 -4 C 1256 -4 1260 -4 1260 0 L 1260 37 C 1260 37 1260 41 1256 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="1236" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="1236px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 1236px; max-width: 1236px;"><p>记<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="script">A</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">\mathscr{A}_k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.22925em;">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.2293em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>为与第k次试验有关的事件全体，若对于任意<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msup><mo>∈</mo><msub><mi mathvariant="script">A</mi><mn>1</mn></msub><mo separator="true">,</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msup><mo>∈</mo><msub><mi mathvariant="script">A</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></msup><mo>∈</mo><msub><mi mathvariant="script">A</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">A^{(1)} \in \mathscr{A}_1,A^{(2)} \in \mathscr{A}_2,\dots,A^{(n)} \in \mathscr{A}_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9271em;vertical-align:-0.0391em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0824em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.22925em;">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.2293em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">2</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0824em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.22925em;">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.2293em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">n</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.85em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.22925em;">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.2293em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>均成立<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msup><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msup><mo>…</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>…</mo><mi>P</mi><mo stretchy="false">(</mo><msup><mi>A</mi><mrow><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(A^{(1)}A^{(2)} \dots A^{(n)}) = P(A^{(1)}) P(A^{(2)}) \dots P(A^{(n)})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">2</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">n</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">1</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">2</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">n</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span>，则称试验<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>E</mi><mn>1</mn></msub><mo separator="true">,</mo><msub><mi>E</mi><mn>2</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>E</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">E_1,E_2,\dots,E_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>是相互独立的</p></div></foreignObject></g><g data-node-id="_xvadgjCv5_QEY5_tR8FR" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,918,-1181.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>重复独立试验</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,113,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="sG0eTKWmnqUcnr6_In64t" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1062,-1296.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 510 0 L 510 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 502 0 C 502 0 510 0 510 8 L 510 23 C 510 23 510 31 502 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 510 -4 C 510 -4 514 -4 514 0 L 514 31 C 514 31 514 35 510 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="490" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在同样条件下<strong>重复试验</strong>，<strong>有关事件的概率保持不变</strong>，而且各次试验是<strong>相互独立</strong>的</p></div></foreignObject></g><g data-node-id="d61J8jIoTGEtILLqCSfil" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1062,-1066.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>最简单的重复独立实验</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="8vRF3kDEF1KF_bCR2IcxS" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1262,-1066.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>伯努利试验</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="GP5UXZ90V-rXwAWPfjmJ3" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1392,-1139.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="FiwGkSpTJI4hEK4M4BpPy" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1480,-1150.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 27 L 0 0 L 520 0 L 520 54 L 0 54 L 0 27 Z"/><path d="M 0 27 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 46 C 520 46 520 54 512 54 L 8 54 C 8 54 0 54 0 46 L 0 27 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 27 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 54 C 524 54 524 58 520 58 L 0 58 C 0 58 -4 58 -4 54 L -4 27 Z" fill="none"/><foreignObject width="500" height="40" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>把事件域取为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">F</mi><mo>=</mo><mrow><mo fence="true">{</mo><mi mathvariant="normal">∅</mi><mo separator="true">,</mo><mi>A</mi><mo separator="true">,</mo><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mo separator="true">,</mo><mi mathvariant="normal">Ω</mi><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">\mathscr{F} = \left\{ \emptyset, A, \overline{A}, \Omega \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2333em;vertical-align:-0.35em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">{</span></span><span class="mord">∅</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">A</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">Ω</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">}</span></span></span></span></span></span></span>，并称出现A为“成功”，出现<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span></span>为“失败”，这种只有两个可能结果的试验称为伯努利试验</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,27)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="6VeF379rzeGtiEPNjVgsk" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2040,-1195.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 479 0 L 479 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 471 0 C 471 0 479 0 479 8 L 479 28 C 479 28 479 36 471 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 479 -4 C 479 -4 483 -4 483 0 L 483 36 C 483 36 483 40 479 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="459" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>有关事件的概率保持不变，重复进行n次，则称为n重伯努利试验，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>E</mi><mi>n</mi></msup></mrow><annotation encoding="application/x-tex">E^n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,488,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="esnnHsXgDKkalbxh6QHpn" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2559,-1255.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>各次试验相互独立</p></div></foreignObject></g><g data-node-id="6lRLPspsZI1ArVQqHUt81" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2559,-1214.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 249 0 L 249 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 241 0 C 241 0 249 0 249 8 L 249 23 C 249 23 249 31 241 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 249 -4 C 249 -4 253 -4 253 0 L 253 31 C 253 31 253 35 249 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="229" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>A在每次试验中出现的概率p保持不变</p></div></foreignObject></g><g data-node-id="E_hJfluBZjxxbggP29Sn-" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2559,-1173.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17 L 0 0 L 295 0 L 295 34 L 0 34 L 0 17 Z"/><path d="M 0 17 L 0 8 C 0 8 0 0 8 0 L 287 0 C 287 0 295 0 295 8 L 295 26 C 295 26 295 34 287 34 L 8 34 C 8 34 0 34 0 26 L 0 17 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17 L -4 0 C -4 0 -4 -4 0 -4 L 295 -4 C 295 -4 299 -4 299 0 L 299 34 C 299 34 299 38 295 38 L 0 38 C 0 38 -4 38 -4 34 L -4 17 Z" fill="none"/><foreignObject width="275" height="20" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>每次试验至多出现两个可能结果之一：A或<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="xSFhGDuti169sivDjbsnj" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2559,-1129.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 113 0 L 113 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 105 0 C 105 0 113 0 113 8 L 113 23 C 113 23 113 31 105 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 113 -4 C 113 -4 117 -4 117 0 L 117 31 C 117 31 117 35 113 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="93" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>共进行n次试验</p></div></foreignObject></g><g data-node-id="scePQtZMLTcM0-FQ-_oFH" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2040,-1088.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 511 0 L 511 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 503 0 C 503 0 511 0 511 8 L 511 28 C 511 28 511 36 503 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 511 -4 C 511 -4 515 -4 515 0 L 515 36 C 515 36 515 40 511 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="491" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>有关事件的概率保持不变，重复进行<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">∞</span></span></span></span></span>次，则称为可列重伯努利试验，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>E</mi><mi mathvariant="normal">∞</mi></msup></mrow><annotation encoding="application/x-tex">E^{\infty}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="8fvBzGXUOUYt3nq1ot0P6" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1392,-993.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>直线上的随机游动</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="PzqSdfM9lDffqpEosdvjr" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1564,-1023.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 45.5 L 0 0 L 520 0 L 520 91 L 0 91 L 0 45.5 Z"/><path d="M 0 45.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 83 C 520 83 520 91 512 91 L 8 91 C 8 91 0 91 0 83 L 0 45.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 45.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 91 C 524 91 524 95 520 95 L 0 95 C 0 95 -4 95 -4 91 L -4 45.5 Z" fill="none"/><foreignObject width="500" height="77" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>考虑x轴上的一个质点，假定它只能位于整数点，在时刻<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">t = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>时，它处于初始位置a（a是整数），以后每隔单位时间，它总受到一个外力的随机作用 ，使位置发生变化，分别以概率p及概率<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">q =1 -p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span></span>向正的或负的方向移动一个单位，我们所关心的是质点在时刻t=n时的位置，用这种方式描述的质点运动称为<strong>随机游动</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,45.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="oXHPzSeytrTp_lgNPKnwO" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2124,-1042.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 244 0 L 244 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 236 0 C 236 0 244 0 244 8 L 244 23 C 244 23 244 31 236 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 244 -4 C 244 -4 248 -4 248 0 L 248 31 C 248 31 248 35 244 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="224" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>质点可以在整个数轴的整数点上游动</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,253,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="nYlNLgk-7vQQE6nXyXU8l" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2408,-1042.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>无限制随机游动</p></div></foreignObject></g><g data-node-id="C2Q7mTIlEh8QCZHbY_8lg" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2124,-1001.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 393 0 L 393 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 385 0 C 385 0 393 0 393 8 L 393 23 C 393 23 393 31 385 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 393 -4 C 393 -4 397 -4 397 0 L 397 31 C 397 31 397 35 393 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="373" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在某点d设有一吸收壁，质点到达这一点即被吸收而不再游动</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,402,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="djmBOl3Kqr1bFyzy-oMK3" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2557,-1001.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 183 0 L 183 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 175 0 C 175 0 183 0 183 8 L 183 23 C 183 23 183 31 175 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 183 -4 C 183 -4 187 -4 187 0 L 187 31 C 187 31 187 35 183 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="163" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在d点有吸收壁的随机游动</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,192,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="1NoMRaKOpY8MOQ0SOlQho" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2780,-1001.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>相关问题：赌徒输光</p></div></foreignObject></g><g data-node-id="vq24PyovUPesxYZKHxRnB" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2124,-960.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 95 0 L 95 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 87 0 C 87 0 95 0 95 8 L 95 40 C 95 40 95 48 87 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 95 -4 C 95 -4 99 -4 99 0 L 99 48 C 99 48 99 52 95 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="75" height="34" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo><mi>q</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mrow><annotation encoding="application/x-tex">p=q=\dfrac{1}{2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,104,24)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="M3H-mJLLfbFBX0aPVQQfy" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2259,-952.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对称的随机游动</p></div></foreignObject></g><g data-node-id="crw3gcv81dc0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,694,975.6)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一维随机变量及其分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="W7pnwzWhE9X163W3F7jts" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,894,-723.4)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机变量</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="GVdbqEDHdHL8g9tsdj-5p" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1010,-850.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>简单定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="hBWWGXz37l0B6r4EdZTE-" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1126,-872.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 37.5 L 0 0 L 520 0 L 520 75 L 0 75 L 0 37.5 Z"/><path d="M 0 37.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 67 C 520 67 520 75 512 75 L 8 75 C 8 75 0 75 0 67 L 0 37.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 37.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 75 C 524 75 524 79 520 79 L 0 79 C 0 79 -4 79 -4 75 L -4 37.5 Z" fill="none"/><foreignObject width="500" height="61" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义在样本空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Ω</span></span></span></span></span>上的实值函数称为随机变量，可用大写字母<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo separator="true">,</mo><mi>Y</mi><mo separator="true">,</mo><mi>Z</mi></mrow><annotation encoding="application/x-tex">X,Y,Z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">Y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">Z</span></span></span></span></span>等表示，亦可用希腊字母<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo separator="true">,</mo><mi>η</mi><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">\xi,\eta,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>等表示，表示试验的结果，其取值常用小写字母<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo separator="true">,</mo><mi>z</mi></mrow><annotation encoding="application/x-tex">x,y,z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></span>表示</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,37.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="_T0lgPjnlRby3tt9J2SbW" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1686,-853.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 284 0 L 284 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 276 0 C 276 0 284 0 284 8 L 284 28 C 284 28 284 36 276 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 284 -4 C 284 -4 288 -4 288 0 L 288 36 C 288 36 288 40 284 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="264" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>例：<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo>=</mo><mi>X</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">X = X(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>或<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo>=</mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi = \xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span></span></span></span></span>为样本点</p></div></foreignObject></g><g data-node-id="KtGR9D3JPRFFGji91I5HV" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1010,-762.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>精确定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="IJDubNre5KntIO7Tt9RCY" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1126,-776.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29.5 L 0 0 L 520 0 L 520 59 L 0 59 L 0 29.5 Z"/><path d="M 0 29.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 51 C 520 51 520 59 512 59 L 8 59 C 8 59 0 59 0 51 L 0 29.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 59 C 524 59 524 63 520 63 L 0 63 C 0 63 -4 63 -4 59 L -4 29.5 Z" fill="none"/><foreignObject width="500" height="45" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>设<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>是定义于概率空间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">Ω</mi><mo separator="true">,</mo><mi mathvariant="script">F</mi><mo separator="true">,</mo><mi>P</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(\Omega,\mathscr{F},P)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">Ω</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mclose">)</span></span></span></span></span>上的单值实函数，如果对于直线上任一博雷尔点集B，有<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mo fence="true">{</mo><mi>ω</mi><mo>:</mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>∈</mo><mi>B</mi><mo fence="true">}</mo></mrow><mo>∈</mo><mi mathvariant="script">F</mi></mrow><annotation encoding="application/x-tex">\left\{ \omega:\xi(\omega) \in B \right\} \in \mathscr{F}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose delimcenter" style="top:0em;">}</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7em;"></span><span class="mord mathscr" style="margin-right:0.13634em;">F</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="sEM_u4YHjVwvWUHUshvcZ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1686,-787.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 137 0 L 137 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 129 0 C 129 0 137 0 137 8 L 137 28 C 137 28 137 36 129 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 137 -4 C 137 -4 141 -4 141 0 L 141 36 C 141 36 141 40 137 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="117" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>为随机变量</p></div></foreignObject></g><g data-node-id="Osb2bE9qakf5zpdqw3g25" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1686,-741.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 300 0 L 300 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 292 0 C 292 0 300 0 300 8 L 300 28 C 300 28 300 36 292 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 300 -4 C 300 -4 304 -4 304 0 L 304 36 C 304 36 304 40 300 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="280" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>∈</mo><mi>B</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\xi(\omega) \in B)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mclose">)</span></span></span></span></span>为随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>的概率分布</p></div></foreignObject></g><g data-node-id="bC1Czq5nlIx-5Ch926I-O" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1010,-687.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>离散型随机变量</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="CC6pQxD2kk7IStHlU5aOC" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1168,-687.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="wk7i6bn8WEDq7KXHT1Fsf" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1256,-695.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>试验结果（随机变量）可能的取值为有限个或可列个，能把结果一一列举出来，这种类型的随机变量称为离散型随机变量</p></div></foreignObject></g><g data-node-id="Uz1Rj5b3qcg-leHGe60oN" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1010,-596.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>连续型随机变量</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="1n8TUbzudf_ViCnLLl0sI" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1168,-596.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="ouFV3_fAjmAqmPCK_EjHo" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1256,-637.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 28 L 0 0 L 520 0 L 520 56 L 0 56 L 0 28 Z"/><path d="M 0 28 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 48 C 520 48 520 56 512 56 L 8 56 C 8 56 0 56 0 48 L 0 28 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 28 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 56 C 524 56 524 60 520 60 L 0 60 C 0 60 -4 60 -4 56 L -4 28 Z" fill="none"/><foreignObject width="500" height="42" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>试验结果（随机变量）可能的取值不止可列个值，其值能取某个区间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>c</mi><mo separator="true">,</mo><mi>d</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[c,d]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal">c</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mclose">]</span></span></span></span></span>或<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(-\infty,+\infty)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">−</span><span class="mord">∞</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">+</span><span class="mord">∞</span><span class="mclose">)</span></span></span></span></span>的一切值，这种类型的 随机变量称为连续型随机变量</p></div></foreignObject></g><g data-node-id="sgIRyMEK0dfr8JsEKXuRN" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1256,-571.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 24 L 0 0 L 520 0 L 520 48 L 0 48 L 0 24 Z"/><path d="M 0 24 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 40 C 520 40 520 48 512 48 L 8 48 C 8 48 0 48 0 40 L 0 24 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 24 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 48 C 524 48 524 52 520 52 L 0 52 C 0 52 -4 52 -4 48 L -4 24 Z" fill="none"/><foreignObject width="500" height="34" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于连续型随机变量，所关心的不是随机变量取某个特定值的概率，而是取某个区间(a,b)或若干个这种区间的概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,24)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="pHav7zTCzlunEXaHBeG8b" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1816,-563.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 575 0 L 575 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 567 0 C 567 0 575 0 575 8 L 575 23 C 575 23 575 31 567 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 575 -4 C 575 -4 579 -4 579 0 L 579 31 C 579 31 579 35 575 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="555" height="17" x="0" y="0" class="text-obj" maxwidth="555px" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 555px; max-width: 555px;"><p>应当要求这些区间对应的集合应当有概率而言，就要求上述集合属于事件域，即均为事件</p></div></foreignObject></g><g data-node-id="m9vzCN9zHJgkDVTaDwFSy" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,894,-500.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分布函数的定义</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="8AA8SvyaPRVS0d7PReVdY" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1052,-513.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mrow><mo fence="true">{</mo><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>x</mi><mo fence="true">}</mo></mrow><mo separator="true">,</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>≤</mo><mi>x</mi><mo>≤</mo><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">F(X) = P \left\{ \xi(\omega) \leq x \right\},-\infty \leq x \leq \infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">x</span><span class="mclose delimcenter" style="top:0em;">}</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mord">∞</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">∞</span></span></span></span></span>为随机变量的分布函数，称“随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span></span></span></span></span>服从分布函数<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>”，记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo stretchy="false">(</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>∼</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi(\omega) \sim F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>或<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo>∼</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi \sim F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="r8Gw5Kq55V70lUngs7wsd" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,894,-362.1)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分布函数的基本性质</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,155,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="ZDWdAzZi-dojvNDYyjHya" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1080,-443.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>单调性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="CpN2KFvTzqWbd9ofEL73k" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1182,-445.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 193 0 L 193 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 185 0 C 185 0 193 0 193 8 L 193 28 C 193 28 193 36 185 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 193 -4 C 193 -4 197 -4 197 0 L 197 36 C 197 36 197 40 193 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="173" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>&lt;</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">a&lt;b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span></span>，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(a) \leq F(b)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,202,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="D6YJVlK5EqLmoFHHFQGR1" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1415,-445.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 266 0 L 266 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 258 0 C 258 0 266 0 266 8 L 266 28 C 266 28 266 36 258 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 266 -4 C 266 -4 270 -4 270 0 L 270 36 C 270 36 270 40 266 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="246" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mrow><mo fence="true">{</mo><mi>a</mi><mo>&lt;</mo><mi>ξ</mi><mo>≤</mo><mi>b</mi><mo fence="true">}</mo></mrow><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">F(b) - F(a) = P \left\{ a &lt; \xi \leq b \right\} \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">b</span><span class="mclose delimcenter" style="top:0em;">}</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="h0Gw_110EE3QCF8pfzJke" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1080,-374.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>有界性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="YbDfn-xXhkl-uW0XRi6f0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1182,-399.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 235 0 L 235 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 227 0 C 227 0 235 0 235 8 L 235 28 C 235 28 235 36 227 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 235 -4 C 235 -4 239 -4 239 0 L 239 36 C 239 36 239 40 235 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="215" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo><mo>=</mo><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mo>−</mo><mi mathvariant="normal">∞</mi></mrow></msub><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">F(-\infty) = lim_{n \to -\infty} F(x) = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord">−</span><span class="mord">∞</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2583em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">−</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="Qd4thm61psFTNbXrEjlbO" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1182,-353.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 235 0 L 235 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 227 0 C 227 0 235 0 235 8 L 235 28 C 235 28 235 36 227 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 235 -4 C 235 -4 239 -4 239 0 L 239 36 C 239 36 239 40 235 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="215" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo><mo>=</mo><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>n</mi><mo>→</mo><mo>+</mo><mi mathvariant="normal">∞</mi></mrow></msub><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">F(+\infty) = lim_{n \to +\infty} F(x) = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord">+</span><span class="mord">∞</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2583em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">→</span><span class="mord mtight">+</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="Lz2VUadymTID2GUBsEqNp" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1080,-280.9)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>连续性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="uPNTFrbTUFZUsTe_wIvTF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1182,-305.2)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>右连续性</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="38l9qTXZNnzqlqqNjtDTS" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1298,-307.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 159 0 L 159 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 151 0 C 151 0 159 0 159 8 L 159 28 C 159 28 159 36 151 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 159 -4 C 159 -4 163 -4 163 0 L 163 36 C 163 36 163 40 159 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="139" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>+</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x_0 + 0) = F(x_0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="iGhXjPp2jITE2oEQ9_tTu" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1182,-261.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 342 0 L 342 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 334 0 C 334 0 342 0 342 8 L 342 28 C 342 28 342 36 334 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 342 -4 C 342 -4 346 -4 346 0 L 346 36 C 346 36 346 40 342 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="322" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>左连续性（若分布函数定义为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>&lt;</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x) = P(\xi &lt; x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span>）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,351,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="wI_kuYOHkXgDcaYRh6r_r" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1564,-261.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 159 0 L 159 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 151 0 C 151 0 159 0 159 8 L 159 28 C 159 28 159 36 151 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 159 -4 C 159 -4 163 -4 163 0 L 163 36 C 163 36 163 40 159 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="139" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mn>0</mn></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x_0 - 0) = F(x_0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="TsuMKcexvxIcTGs9UIsDM" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1753,-352)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 440 0 L 440 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 432 0 C 432 0 440 0 440 8 L 440 23 C 440 23 440 31 432 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 440 -4 C 440 -4 444 -4 444 0 L 444 31 C 444 31 444 35 440 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="420" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>满足这三条性质的函数一定是某个随机变量的分布函数（充要条件）</p></div></foreignObject></g><g data-node-id="2eH6vUM-l4jKDfKgSN0SX" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,894,4.1)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 202 0 L 202 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 194 0 C 194 0 202 0 202 8 L 202 23 C 202 23 202 31 194 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 202 -4 C 202 -4 206 -4 206 0 L 206 31 C 206 31 206 35 202 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="182" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>右连续的分布函数与概率计算</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,211,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="WIg9TSBCKX-JyKLe_nbrh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,-215.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 230 0 L 230 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 222 0 C 222 0 230 0 230 8 L 230 28 C 230 28 230 36 222 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 230 -4 C 230 -4 234 -4 234 0 L 234 36 C 234 36 234 40 230 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="210" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\xi = a) = F(a) - F(a - 0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="g5qkloi1n533xyQShkV2O" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,-169.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 144 0 L 144 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 136 0 C 136 0 144 0 144 8 L 144 28 C 144 28 144 36 136 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 144 -4 C 144 -4 148 -4 148 0 L 148 36 C 148 36 148 40 144 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="124" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>≤</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\xi \leq a) = F(a)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="ZPQLLnGe1Ozo2V0Xu0WzG" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,-123.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 203 0 L 203 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 195 0 C 195 0 203 0 203 8 L 203 28 C 203 28 203 36 195 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 203 -4 C 203 -4 207 -4 207 0 L 207 36 C 207 36 207 40 203 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="183" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>≥</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\xi \geq a) = 1 - F(a-0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="tlTProAIGZtcxideW6hee" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,-77.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 173 0 L 173 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 165 0 C 165 0 173 0 173 8 L 173 28 C 173 28 173 36 165 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 173 -4 C 173 -4 177 -4 177 0 L 177 36 C 177 36 177 40 173 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="153" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>&lt;</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\xi &lt; a) = F(a - 0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="_RWm9UjMKHRX9SBOfLf9R" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,-31.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 173 0 L 173 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 165 0 C 165 0 173 0 173 8 L 173 28 C 173 28 173 36 165 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 173 -4 C 173 -4 177 -4 177 0 L 177 36 C 177 36 177 40 173 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="153" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>&gt;</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(\xi &gt; a) = 1 - F(a)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="5koh5EFLvcoSxb-owyoEh" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,14.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 258 0 L 258 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 250 0 C 250 0 258 0 258 8 L 258 28 C 258 28 258 36 250 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 258 -4 C 258 -4 262 -4 262 0 L 262 36 C 262 36 262 40 258 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="238" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>a</mi><mo>&lt;</mo><mi>ξ</mi><mo>&lt;</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(a &lt; \xi &lt; b) = F(b-0) - F(a)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="A4Dia6tmwJz7QTBpgEwIF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,60.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 229 0 L 229 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 221 0 C 221 0 229 0 229 8 L 229 28 C 229 28 229 36 221 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 229 -4 C 229 -4 233 -4 233 0 L 233 36 C 233 36 233 40 229 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="209" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>a</mi><mo>&lt;</mo><mi>ξ</mi><mo>≤</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(a &lt; \xi \leq b) = F(b) - F(a)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="1IP0TwiX8INgyokJHIWmJ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,106.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 287 0 L 287 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 279 0 C 279 0 287 0 287 8 L 287 28 C 287 28 287 36 279 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 287 -4 C 287 -4 291 -4 291 0 L 291 36 C 291 36 291 40 287 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="267" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>a</mi><mo>≤</mo><mi>ξ</mi><mo>&lt;</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(a \leq \xi &lt; b) = F(b-0) - F(a-0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="cC0Lpu6Nan2O9W9twLoTO" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,152.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 258 0 L 258 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 250 0 C 250 0 258 0 258 8 L 258 28 C 258 28 258 36 250 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 258 -4 C 258 -4 262 -4 262 0 L 262 36 C 262 36 262 40 258 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="238" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>a</mi><mo>≤</mo><mi>ξ</mi><mo>≤</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">P(a \leq \xi \leq b) = F(b) - F(a - 0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="QtcbQAmV9f0t70HdjrxUE" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1136,223.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 148 0 L 148 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 140 0 C 140 0 148 0 148 8 L 148 23 C 148 23 148 31 140 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 148 -4 C 148 -4 152 -4 152 0 L 152 31 C 152 31 152 35 148 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="128" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>当F(x)在a,b处连续时</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,157,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="ydka1WgI67P427HBwIZjP" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1324,198.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 143 0 L 143 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 135 0 C 135 0 143 0 143 8 L 143 28 C 143 28 143 36 135 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 143 -4 C 143 -4 147 -4 147 0 L 147 36 C 147 36 147 40 143 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="123" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>a</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(a) = F(a - 0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="g8i7PACUwQ7wS7773aOJF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1324,244.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 139 0 L 139 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 131 0 C 131 0 139 0 139 8 L 139 28 C 139 28 139 36 131 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 139 -4 C 139 -4 143 -4 143 0 L 143 36 C 143 36 143 40 139 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="119" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>b</mi><mo>−</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(b) = F(b - 0)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="S-pp0qq8mjk256RS17IQv" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,894,773.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>离散型随机变量的分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="g845ywxU4xR9snWZGZiGN" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,323.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>概率分布与分布列</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,141,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Q62oSMp9NO3sJZOkRrJ72" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1266,321.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 694 0 L 694 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 686 0 C 686 0 694 0 694 8 L 694 28 C 694 28 694 36 686 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 694 -4 C 694 -4 698 -4 698 0 L 698 36 C 698 36 698 40 694 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="674" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="674px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 674px; max-width: 674px;"><p>设<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">{</mo><mi>ξ</mi><mo>=</mo><msub><mi>x</mi><mi>i</mi></msub><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{ \xi = x_i \right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span></span>为随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>的所有可能值，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span>是<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>取<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>的概率，即<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>p</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(\xi = x_i) = p(x_i),i = 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class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" 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aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">{</span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mclose delimcenter" style="top:0em;">}</span></span></span></span></span></span>称为随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>的概率分布</p></div></foreignObject></g><g data-node-id="cU_PUjd9qvvDUQu5u4NK1" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2000,357.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 230 0 L 230 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 222 0 C 222 0 230 0 230 8 L 230 23 C 230 23 230 31 222 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 230 -4 C 230 -4 234 -4 234 0 L 234 31 C 234 31 234 35 230 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="210" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 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stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>p</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mo lspace="0em" rspace="0em">…</mo></mstyle></mtd></mtr></mtable></menclose></mrow><annotation encoding="application/x-tex">\begin{array}{c|ccccc}

\hline

\xi &amp; x_1 &amp; x_2 &amp; \dots &amp; x_n &amp; \dots \\[0.5em]

\hline

P &amp; p(x_1) &amp; p(x_2) &amp; \dots &amp; p(x_n) &amp; \dots \\[0.5em]
\hline
\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.44em;vertical-align:-1.45em;"></span><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.99em;"><span style="top:-3.95em;"><span class="pstrut" style="height:3.95em;"></span><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.95em;"><span style="top:-4.11em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="vertical-separator" style="height:3.4em;border-right-width:0.04em;border-right-style:solid;margin:0 -0.02em;vertical-align:-1.45em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.95em;"><span style="top:-4.11em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.95em;"><span style="top:-4.11em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.95em;"><span style="top:-4.11em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="minner">…</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.95em;"><span style="top:-4.11em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.95em;"><span style="top:-4.11em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="minner">…</span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="minner">…</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span style="top:-2.5em;"><span class="pstrut" style="height:3.95em;"></span><span class="hline" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.2em;"><span class="pstrut" style="height:3.95em;"></span><span class="hline" style="border-bottom-width:0.04em;"></span></span><span style="top:-5.9em;"><span class="pstrut" style="height:3.95em;"></span><span class="hline" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="434o-1VxPK5_3s29kkScq" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,421.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分布函数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="aAPE3-GOuJhtCO9h7CwFi" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1210,419.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 260 0 L 260 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 252 0 C 252 0 260 0 260 8 L 260 28 C 260 28 260 36 252 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 260 -4 C 260 -4 264 -4 264 0 L 264 36 C 264 36 264 40 260 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="240" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>≤</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mo>∑</mo><mrow><msub><mi>x</mi><mi>k</mi></msub><mo>≤</mo><mi>x</mi></mrow></msub><mi>p</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>k</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x) = P(\xi \leq x) = \sum_{x_k \leq x} p(x_k)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1556em;vertical-align:-0.4056em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1455em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3488em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1512em;"><span></span></span></span></span></span></span><span class="mrel mtight">≤</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4056em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,269,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="VhQ6hv_vbMkBvdeyK1TfN" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1510,421.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>跳跃函数</p></div></foreignObject></g><g data-node-id="4qLkM8p3g7FmhUd2LuyJb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,1223.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>常见离散型分布</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="s9MaxxjMeb32uRN6KYstq" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,482.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>退化分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="xZFtPGpM1TBPeUzgYrqX9" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,471.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 520 0 L 520 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 45 C 520 45 520 53 512 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 53 C 524 53 524 57 520 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="500" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span></span></span></span></span>只取常数值c，即<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>α</mi><mo>=</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\alpha = c) = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span>，这样的<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span></span></span></span></span>并不随机，我们把它看作随机变量的退化情况，因此称之为退化分布，又称单点分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,26.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" 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displaystyle="false"><mrow><mo separator="true">,</mo><mi>x</mi><mo>≥</mo><mi>c</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">I_c(x) = \begin{cases}

0 &amp;, x &lt; c \\

1 &amp;, x \geq c

\end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3em;vertical-align:-1.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">c</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="W36UOSBC84JlTUumtiYk7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,565.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>伯努利分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="sgXdao6OTIUgL2YoOShtA" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,552.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在一次试验中，事件A出现的概率为p，不出现的概率为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mo>=</mo><mn>1</mn><mo>−</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">q = 1 - p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span></span></span></span></span>，若以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span></span>记事件A出现的次数，则仅<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span></span>取0,1两值，称此分布为伯努利分布，亦称两点分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="PeI3KBVtwt0VT-msIv29n" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,540.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 223 0 L 223 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 215 0 C 215 0 223 0 223 8 L 223 28 C 223 28 223 36 215 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 223 -4 C 223 -4 227 -4 227 0 L 227 36 C 227 36 227 40 223 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="203" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>β</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>p</mi><mi>k</mi></msup><msup><mi>q</mi><mrow><mn>1</mn><mo>−</mo><mi>k</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">P(\beta = k) = p^k q^{1-k},k=0,1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0435em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="TGB6rh1UclBYNso5z78xG" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,586.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 121 0 L 121 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 113 0 C 113 0 121 0 121 8 L 121 28 C 121 28 121 36 113 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 121 -4 C 121 -4 125 -4 125 0 L 125 36 C 125 36 125 40 121 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="101" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>记</mtext><mi>β</mi><mo>∼</mo><mi>B</mi><mo stretchy="false">(</mo><mn>1</mn><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">记\beta \sim B(1,p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord cjk_fallback">记</span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mopen">(</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="e5TqP6VMtebbVVu6PqIg0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,777.6)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>二项分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="zL6-3Iz2zgUs7dnNy3Vlf" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,644.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在n重伯努利试验中，若以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">μ</span></span></span></span></span>记成功的次数，则它是一个随机变量，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">μ</span></span></span></span></span>取值为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">0,1,2,\dots,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span></span></span></span></span>，其对应的概率服从二项分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="gcIEvcHfIZjKop1mcWqbJ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,632.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 293 0 L 293 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 285 0 C 285 0 293 0 293 8 L 293 28 C 293 28 293 36 285 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 293 -4 C 293 -4 297 -4 297 0 L 297 36 C 297 36 297 40 293 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="273" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>μ</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mi>n</mi><mi>k</mi></msubsup><msup><mi>p</mi><mi>k</mi></msup><msup><mi>q</mi><mrow><mn>1</mn><mo>−</mo><mi>k</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">P(\mu = k) = C_{n}^{k} p^k q^{1-k},k = 1,2,\dots,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">μ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0961em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="149UPoaNLzg1S1fQuDs4H" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,678.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 123 0 L 123 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 115 0 C 115 0 123 0 123 8 L 123 28 C 123 28 123 36 115 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 123 -4 C 123 -4 127 -4 127 0 L 127 36 C 127 36 127 40 123 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="103" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>记</mtext><mi>μ</mi><mo>∼</mo><mi>B</mi><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">记\mu \sim B(n,p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord cjk_fallback">记</span><span class="mord mathnormal">μ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="qpmOru8kAPQbaPZatUnX7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,759.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">B_k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>记n重伯努利试验中事件A正好出现k次这一事件，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">A_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>为第i次试验中事件A发生，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\overline{A}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>为第i次实验中事件<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8833em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span></span></span></span></span>发生，记<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>n</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">b(k;n,p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span>为该事件的概率</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="R0BWSXZVj3ZJeh-924Li7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,724.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 498 0 L 498 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 490 0 C 490 0 498 0 498 8 L 498 28 C 498 28 498 36 490 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 498 -4 C 498 -4 502 -4 502 0 L 502 36 C 502 36 502 40 498 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="478" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>B</mi><mi>k</mi></msub><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>A</mi><mn>2</mn></msub><mo>…</mo><msub><mi>A</mi><mi>k</mi></msub><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>…</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mi>n</mi></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mn>1</mn></msub><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mn>2</mn></msub><mo>…</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mrow><mi>n</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>…</mo><msub><mi>A</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">B_k = A_1A_2 \dots A_k \overline{A}_{k+1} \dots \overline{A}_n + \dots + \overline{A}_1 \overline{A}_2 \dots \overline{A}_{n-k} \overline{A}_{n-k+1}  \dots A_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0917em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0917em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="q-FF8l_WEyCYPFd_W6R39" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,770.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 358 0 L 358 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 350 0 C 350 0 358 0 358 8 L 358 28 C 358 28 358 36 350 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 358 -4 C 358 -4 362 -4 362 0 L 362 36 C 362 36 362 40 358 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="338" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>n</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>B</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mi>n</mi><mi>k</mi></msubsup><msup><mi>p</mi><mi>k</mi></msup><msup><mi>q</mi><mrow><mn>1</mn><mo>−</mo><mi>k</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">b(k;n,p) = P(B_k) = C_{n}^{k} p^k q^{1-k},k = 1,2,\dots,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0961em;vertical-align:-0.247em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,367,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="8F_0Wf-46JCutQ_DPBUyE" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2326,772.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>二项展开式系数</p></div></foreignObject></g><g data-node-id="vhAuDNwfw2Ku5tu2_UxCX" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,816.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 377 0 L 377 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 369 0 C 369 0 377 0 377 8 L 377 28 C 377 28 377 36 369 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 377 -4 C 377 -4 381 -4 381 0 L 381 36 C 381 36 381 40 377 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="357" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></msubsup><mi>b</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>n</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></msubsup><msubsup><mi>C</mi><mi>n</mi><mi>k</mi></msubsup><msup><mi>p</mi><mi>k</mi></msup><msup><mi>q</mi><mrow><mn>1</mn><mo>−</mo><mi>k</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mi>q</mi><mo>+</mo><mi>p</mi><msup><mo stretchy="false">)</mo><mi>n</mi></msup><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\sum_{k=0}^{n} b(k;n,p) = \sum_{k=0}^{n} C_{n}^{k} p^k q^{1-k} = (q+p)^n = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1488em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="FJfU402IcWq2hMMS95ysP" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,910.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div 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C 520 45 520 53 512 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 53 C 524 53 524 57 520 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="500" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>当n固定时，二项分布的概率<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>n</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">b(k;n,p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span>先随着k的增大而增大，达到某一极大值后又逐渐下降</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,26.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="rhNawYGLPogojqfbCdINv" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2086,908.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 339 0 L 339 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 331 0 C 331 0 339 0 339 8 L 339 28 C 339 28 339 36 331 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 339 -4 C 339 -4 343 -4 343 0 L 343 36 C 343 36 343 40 339 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="319" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>取<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>&lt;</mo><mi>m</mi><mo>=</mo><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi>p</mi><mo stretchy="false">]</mo><mo>≤</mo><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi>p</mi></mrow><annotation encoding="application/x-tex">(n+1)p - 1 &lt; m = [(n+1)p] \leq (n+1)p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6835em;vertical-align:-0.0391em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mord mathnormal">p</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mord mathnormal">p</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,348,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="vBaCyrnTqA50Ta4UcgeY_" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2465,862.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 98 0 L 98 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 90 0 C 90 0 98 0 98 8 L 98 28 C 98 28 98 36 90 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 98 -4 C 98 -4 102 -4 102 0 L 102 36 C 102 36 102 40 98 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="78" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>k</mi><mo>&lt;</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">0 \leq k &lt; m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,107,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="tW4LTWlQdv59dBJJcZ1Rx" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2603,864.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>单调增加</p></div></foreignObject></g><g data-node-id="iQI13aO0tu7QJ4e3wFCas" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2465,908.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 67 0 L 67 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 59 0 C 59 0 67 0 67 8 L 67 28 C 67 28 67 36 59 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 67 -4 C 67 -4 71 -4 71 0 L 71 36 C 71 36 71 40 67 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="47" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mo>=</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">k = m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,76,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="-MCVOrmL_HBXVmzH2DF9i" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2572,910.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>极大值</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="wgdQPpno0P_GPKfm6qDJ7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2674,910.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 188 0 L 188 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 180 0 C 180 0 188 0 188 8 L 188 23 C 188 23 188 31 180 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 188 -4 C 188 -4 192 -4 192 0 L 192 31 C 192 31 192 35 188 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="168" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>中心项，最可能的成功次数</p></div></foreignObject></g><g data-node-id="Nn2epSlUlcpljoXfcwRVg" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2465,954.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 100 0 L 100 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 92 0 C 92 0 100 0 100 8 L 100 28 C 100 28 100 36 92 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 100 -4 C 100 -4 104 -4 104 0 L 104 36 C 104 36 104 40 100 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="80" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mo>&lt;</mo><mi>k</mi><mo>≤</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">m &lt; k \leq n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8304em;vertical-align:-0.136em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,109,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="3ferj1fXhcXLtTTOcMiy_" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2605,956.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>单调下降</p></div></foreignObject></g><g data-node-id="JbgYHCCJLPFJYPlPBGfO2" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,1148.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>泊松分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Dv3j3tUaXzRJjstscXI85" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,1023.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26 L 0 0 L 688 0 L 688 52 L 0 52 L 0 26 Z"/><path d="M 0 26 L 0 8 C 0 8 0 0 8 0 L 680 0 C 680 0 688 0 688 8 L 688 44 C 688 44 688 52 680 52 L 8 52 C 8 52 0 52 0 44 L 0 26 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26 L -4 0 C -4 0 -4 -4 0 -4 L 688 -4 C 688 -4 692 -4 692 0 L 692 52 C 692 52 692 56 688 56 L 0 56 C 0 56 -4 56 -4 52 L -4 26 Z" fill="none"/><foreignObject width="668" height="38" x="0" y="0" class="text-obj formula-text" maxwidth="668px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 668px; max-width: 668px;"><p>若随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>可取一切非负整数值，且<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msup><mi>λ</mi><mi>k</mi></msup><mrow><mi>k</mi><mo stretchy="false">!</mo></mrow></mfrac></mstyle><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(\xi = k) = \dfrac{\lambda^k}{k!} e^{-\lambda} , k=0,1,2,\dots, \lambda &gt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2121em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">!</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">λ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，则称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>服从泊松分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,697,26)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="jsu4N9ACTIzqsCzTNDDZ_" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2096,1000.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26 L 0 0 L 316 0 L 316 52 L 0 52 L 0 26 Z"/><path d="M 0 26 L 0 8 C 0 8 0 0 8 0 L 308 0 C 308 0 316 0 316 8 L 316 44 C 316 44 316 52 308 52 L 8 52 C 8 52 0 52 0 44 L 0 26 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26 L -4 0 C -4 0 -4 -4 0 -4 L 316 -4 C 316 -4 320 -4 320 0 L 320 52 C 320 52 320 56 316 56 L 0 56 C 0 56 -4 56 -4 52 L -4 26 Z" fill="none"/><foreignObject width="296" height="38" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msup><mi>λ</mi><mi>k</mi></msup><mrow><mi>k</mi><mo stretchy="false">!</mo></mrow></mfrac></mstyle><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(\xi = k) = \dfrac{\lambda^k}{k!} e^{-\lambda} , k=0,1,2,\dots, \lambda &gt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2121em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">!</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">λ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="LEnZGqZFmMet8AXHbaMdv" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2096,1062.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 101 0 L 101 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 93 0 C 93 0 101 0 101 8 L 101 28 C 101 28 101 36 93 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 101 -4 C 101 -4 105 -4 105 0 L 105 36 C 105 36 105 40 101 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="81" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>记<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo>∼</mo><mi>P</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\xi \sim P(\lambda)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">λ</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="ckaN0LOlVwSUl8yYwwTEx" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,1145.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>二项分布的泊松逼近</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,155,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="k-uoQCkWk9MZRAPdqv4Yq" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1554,1108.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26 L 0 0 L 854 0 L 854 52 L 0 52 L 0 26 Z"/><path d="M 0 26 L 0 8 C 0 8 0 0 8 0 L 846 0 C 846 0 854 0 854 8 L 854 44 C 854 44 854 52 846 52 L 8 52 C 8 52 0 52 0 44 L 0 26 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26 L -4 0 C -4 0 -4 -4 0 -4 L 854 -4 C 854 -4 858 -4 858 0 L 858 52 C 858 52 858 56 854 56 L 0 56 C 0 56 -4 56 -4 52 L -4 26 Z" fill="none"/><foreignObject width="834" height="38" x="0" y="0" class="text-obj formula-text" maxwidth="834px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 834px; max-width: 834px;"><p>在独立试验中，以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">p_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>代表事件A在试验中出现的概率，它与试验总数n有关，如果<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><msub><mi>p</mi><mi>n</mi></msub><mo>→</mo><mi>λ</mi></mrow><annotation encoding="application/x-tex">np_n \to \lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span></span>，则当<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">n \to \infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">∞</span></span></span></span></span>时，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>n</mi><mo separator="true">,</mo><msub><mi>p</mi><mi>n</mi></msub><mo stretchy="false">)</mo><mo>→</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msup><mi>λ</mi><mi>k</mi></msup><mrow><mi>k</mi><mo stretchy="false">!</mo></mrow></mfrac></mstyle><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi></mrow></msup></mrow><annotation encoding="application/x-tex">b(k;n,p_n) \to \dfrac{\lambda^k}{k!} e^{-\lambda}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2121em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">!</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">λ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span></span></span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="rTbp_POZ4x5OCL6etYYf6" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1554,1178.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 222 0 L 222 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 214 0 C 214 0 222 0 222 8 L 222 28 C 222 28 222 36 214 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 222 -4 C 222 -4 226 -4 226 0 L 226 36 C 226 36 226 40 222 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="202" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>当p相当小时（一般当<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>≤</mo><mn>0.1</mn></mrow><annotation encoding="application/x-tex">p \leq 0.1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8304em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.1</span></span></span></span></span>）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,231,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="cyBkrvN-bTkPLfAwiN3OG" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1816,1170.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26 L 0 0 L 182 0 L 182 52 L 0 52 L 0 26 Z"/><path d="M 0 26 L 0 8 C 0 8 0 0 8 0 L 174 0 C 174 0 182 0 182 8 L 182 44 C 182 44 182 52 174 52 L 8 52 C 8 52 0 52 0 44 L 0 26 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26 L -4 0 C -4 0 -4 -4 0 -4 L 182 -4 C 182 -4 186 -4 186 0 L 186 52 C 186 52 186 56 182 56 L 0 56 C 0 56 -4 56 -4 52 L -4 26 Z" fill="none"/><foreignObject width="162" height="38" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>n</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo><mo>≈</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>n</mi><mi>p</mi><msup><mo stretchy="false">)</mo><mi>k</mi></msup></mrow><mrow><mi>k</mi><mo stretchy="false">!</mo></mrow></mfrac></mstyle><msup><mi>e</mi><mrow><mo>−</mo><mi>n</mi><mi>p</mi></mrow></msup></mrow><annotation encoding="application/x-tex">b(k;n,p)  \approx \dfrac{(np)^k}{k!} e^{-np}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2121em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5261em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">!</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal">p</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">n</span><span class="mord mathnormal mtight">p</span></span></span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="Jvs1QVvttnB1V_ADEONXL" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,1273.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>泊松过程</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="_lJSjsZiMPI7nT0RInjKb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1484,1232.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>平稳性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="ijhkI6qh50DzjpJ6Yvjr9" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1586,1232.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 258 0 L 258 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 250 0 C 250 0 258 0 258 8 L 258 23 C 258 23 258 31 250 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 258 -4 C 258 -4 262 -4 262 0 L 262 31 C 262 31 262 35 258 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="238" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>过程的概率规律不随时间的推移而改变</p></div></foreignObject></g><g data-node-id="98ip2T3OyWqzUzfBG9JDC" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1484,1273.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 174 0 L 174 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 166 0 C 166 0 174 0 174 8 L 174 23 C 174 23 174 31 166 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 174 -4 C 174 -4 178 -4 178 0 L 178 31 C 178 31 178 35 174 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="154" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>独立增量性（无后效性）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,183,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="rnNnJIn7ZwJAMhE8-WCdC" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1698,1273.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 300 0 L 300 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 292 0 C 292 0 300 0 300 8 L 300 23 C 300 23 300 31 292 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 300 -4 C 300 -4 304 -4 304 0 L 304 31 C 304 31 304 35 300 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="280" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在互不相交的时间区间内过程的进行相互独立</p></div></foreignObject></g><g data-node-id="VotFqFlQxp5C2tjqf2mQ8" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1484,1314.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>普通性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="w5FLLsplKuEkL-NgLLHFN" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1586,1314.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 384 0 L 384 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 376 0 C 376 0 384 0 384 8 L 384 23 C 384 23 384 31 376 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 384 -4 C 384 -4 388 -4 388 0 L 388 31 C 388 31 388 35 384 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="364" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在同一事件瞬间事件发生两次或两次以上实际上是不可能的</p></div></foreignObject></g><g data-node-id="anvj2q_CEXlug5cvORXYZ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,1392.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>超几何分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="5_UhP2YGebQezyB0r83LF" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,1370.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 37.5 L 0 0 L 520 0 L 520 75 L 0 75 L 0 37.5 Z"/><path d="M 0 37.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 67 C 520 67 520 75 512 75 L 8 75 C 8 75 0 75 0 67 L 0 37.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 37.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 75 C 524 75 524 79 520 79 L 0 79 C 0 79 -4 79 -4 75 L -4 37.5 Z" fill="none"/><foreignObject width="500" height="61" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对某批N件产品进行不放回抽样检查，若这批产品中有M件次品，现从整批产品中随机抽取出n件产品，则在这n件产品中出现的次品数<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ν</mi></mrow><annotation encoding="application/x-tex">\nu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.06366em;">ν</span></span></span></span></span>是随机变量，它取值<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">0,1,2,\dots,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span></span></span></span></span>，其概率分布为超几何分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,37.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="0vztsenRpFI6S2yKWNEl9" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,1355.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29.5 L 0 0 L 365 0 L 365 59 L 0 59 L 0 29.5 Z"/><path d="M 0 29.5 L 0 8 C 0 8 0 0 8 0 L 357 0 C 357 0 365 0 365 8 L 365 51 C 365 51 365 59 357 59 L 8 59 C 8 59 0 59 0 51 L 0 29.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29.5 L -4 0 C -4 0 -4 -4 0 -4 L 365 -4 C 365 -4 369 -4 369 0 L 369 59 C 369 59 369 63 365 63 L 0 63 C 0 63 -4 63 -4 59 L -4 29.5 Z" fill="none"/><foreignObject width="345" height="45" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ν</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msubsup><mi>C</mi><mi>M</mi><mi>k</mi></msubsup><msubsup><mi>C</mi><mrow><mi>N</mi><mo>−</mo><mi>M</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msubsup></mrow><msubsup><mi>C</mi><mi>N</mi><mi>n</mi></msubsup></mfrac></mstyle><mo separator="true">,</mo><mn>0</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>≤</mo><mi>N</mi><mo separator="true">,</mo><mi>k</mi><mo>≤</mo><mi>M</mi></mrow><annotation encoding="application/x-tex">P(\nu = k) = \dfrac{C_M^k C_{N-M}^{n-k}}{C_{N}^{n}}, 0 \leq k \leq n \leq N,k \leq M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.06366em;">ν</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.6106em;vertical-align:-0.9795em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6311em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6462em;"><span style="top:-2.4065em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span><span style="top:-3.0448em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2935em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.7419em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.4247em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2753em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8892em;"><span style="top:-2.4065em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3519em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9795em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8304em;vertical-align:-0.136em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="SLqr6UorbEvr8lPMzHtH2" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,1424.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 134 0 L 134 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 126 0 C 126 0 134 0 134 8 L 134 28 C 134 28 134 36 126 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 134 -4 C 134 -4 138 -4 138 0 L 138 36 C 138 36 138 40 134 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="114" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ν</mi><mo>∼</mo><mi>h</mi><mo stretchy="false">(</mo><mi>n</mi><mo separator="true">,</mo><mi>N</mi><mo separator="true">,</mo><mi>M</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\nu \sim h(n,N,M)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.06366em;">ν</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="Xd5edQEG3XL6XSwcwUuSQ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,1604.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>几何分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="7Ykr3Sgv3m25vbAZbtj9b" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,1482.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在成功的概率为p的伯努利试验中，若以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi></mrow><annotation encoding="application/x-tex">\eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span></span></span></span>记成功首次出现时的试验次数，则为随<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi></mrow><annotation encoding="application/x-tex">\eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span></span></span></span>机变量，它可能取的值为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">1,2,3,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>其概率分布为集合分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="geBIUIuuEiw5Z9hh5XZLl" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,1470.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 241 0 L 241 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 233 0 C 233 0 241 0 241 8 L 241 28 C 241 28 241 36 233 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 241 -4 C 241 -4 245 -4 245 0 L 245 36 C 245 36 245 40 241 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="221" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>η</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>q</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>p</mi><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(\eta = k) = q^{k-1} p, k=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0435em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="yp7Gy4dL1qhdLPuAhAPj2" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,1516.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 95 0 L 95 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 87 0 C 87 0 95 0 95 8 L 95 28 C 95 28 95 36 87 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 95 -4 C 95 -4 99 -4 99 0 L 99 36 C 99 36 99 40 95 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="75" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi><mo>∼</mo><mi>G</mi><mi>e</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\eta \sim Ge(p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">G</span><span class="mord mathnormal">e</span><span class="mopen">(</span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="yNKfwID1ejpejJE_UPhtd" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,1616.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 403 0 L 403 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 395 0 C 395 0 403 0 403 8 L 403 28 C 403 28 403 36 395 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 403 -4 C 403 -4 407 -4 407 0 L 407 36 C 407 36 407 40 403 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="383" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>事件<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>W</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">W_k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>为事件A首次出现在第k次试验中，其概率记为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">g(k;p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,412,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="K25oz6DxJH3O44Jo8yxGX" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1811,1562.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 191 0 L 191 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 183 0 C 183 0 191 0 191 8 L 191 28 C 191 28 191 36 183 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 191 -4 C 191 -4 195 -4 195 0 L 195 36 C 195 36 195 40 191 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="171" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>W</mi><mi>k</mi></msub><mo>=</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mn>1</mn></msub><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mn>2</mn></msub><mo>…</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>A</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">W_k = \overline{A}_1 \overline{A}_2 \dots \overline{A}_{k-1} A_k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0917em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="70oCWQxCr_xNrFw8unhMU" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1811,1608.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 563 0 L 563 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 555 0 C 555 0 563 0 563 8 L 563 28 C 563 28 563 36 555 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 563 -4 C 563 -4 567 -4 567 0 L 567 36 C 567 36 567 40 563 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="543" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="543px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 543px; max-width: 543px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>W</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mn>1</mn></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mn>2</mn></msub><mo stretchy="false">)</mo><mo>…</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>A</mi><mo stretchy="true">‾</mo></mover><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msub><mo stretchy="false">)</mo><mi>P</mi><mo stretchy="false">(</mo><msub><mi>A</mi><mi>k</mi></msub><mo stretchy="false">)</mo><mo>=</mo><msup><mi>q</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>p</mi><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">g(k;p) = P(W_k) =  P(\overline{A}_1) P(\overline{A}_2) \dots P(\overline{A}_{k-1}) P(A_k) = q^{k-1} p, k=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1333em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8833em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span></span></span><span style="top:-3.8033em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0435em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="ukeq-HiJ_BBnptGIX1N9Z" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1811,1654.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26 L 0 0 L 414 0 L 414 52 L 0 52 L 0 26 Z"/><path d="M 0 26 L 0 8 C 0 8 0 0 8 0 L 406 0 C 406 0 414 0 414 8 L 414 44 C 414 44 414 52 406 52 L 8 52 C 8 52 0 52 0 44 L 0 26 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26 L -4 0 C -4 0 -4 -4 0 -4 L 414 -4 C 414 -4 418 -4 418 0 L 418 52 C 418 52 418 56 414 56 L 0 56 C 0 56 -4 56 -4 52 L -4 26 Z" fill="none"/><foreignObject width="394" height="38" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>g</mi><mo stretchy="false">(</mo><mi>k</mi><mo separator="true">;</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msup><mi>q</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>p</mi><mo>=</mo><mi>p</mi><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mn>1</mn><mo>−</mo><mi>q</mi></mrow></mfrac></mstyle><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">\sum_{k=1}^{\infty} g(k;p) = \sum_{k=1}^{\infty} q^{k-1} p = p \dfrac{1}{1-q} = 1, k=1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1488em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2019em;vertical-align:-0.8804em;"></span><span class="mord mathnormal">p</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,423,26)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="DzOAMJdR6BWOgtRhFgyx0" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2265,1664.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 132 0 L 132 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 124 0 C 124 0 132 0 132 8 L 132 23 C 132 23 132 31 124 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 132 -4 C 132 -4 136 -4 136 0 L 136 31 C 136 31 136 35 132 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="112" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>几何级数的一般项</p></div></foreignObject></g><g data-node-id="BWsW6yZc7NClQ9TJFRBJD" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,1727.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 146 0 L 146 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 138 0 C 138 0 146 0 146 8 L 146 23 C 146 23 146 31 138 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 146 -4 C 146 -4 150 -4 150 0 L 150 31 C 150 31 150 35 146 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="126" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>几何分布的无记忆性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,155,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="NRLhCp4pX_QeCrXRMoWD8" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1554,1716.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 520 0 L 520 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 45 C 520 45 520 53 512 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 53 C 524 53 524 57 520 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="500" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>假定已知在前m次实验中没有出现成功，那么为了达到首次成功所再需要的等待时间<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>η</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup></mrow><annotation encoding="application/x-tex">\eta'</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9463em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span>，其概率分布依旧为几何分布，与前面的m次失败无关</p></div></foreignObject></g><g data-node-id="ES7cdnnmIE8Iy4svTu16e" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,1832.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>帕斯卡分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="019CFdfaPxtkCxQEF7-3u" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,1779.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在成功的概率为p的伯努利试验中，若以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span></span></span></span>记第r次成功出现时的试验次数，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span></span></span></span>是随机变量，取值为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo separator="true">,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">r,r+1,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>，其概率分布为帕斯卡分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="CGSq9XcTUxJ5owSolDlyz" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,1790.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 312 0 L 312 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 304 0 C 304 0 312 0 312 8 L 312 28 C 312 28 312 36 304 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 312 -4 C 312 -4 316 -4 316 0 L 316 36 C 316 36 316 40 312 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="292" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ζ</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msup><mi>p</mi><mi>r</mi></msup><msup><mi>q</mi><mrow><mi>k</mi><mo>−</mo><mi>r</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mi>r</mi><mo separator="true">,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(\zeta = k) = C_{k-1}^{r-1} p^r q^{k-r}, k = r, r+1, \dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2139em;vertical-align:-0.3596em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.3987em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3596em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="L-Vrx2GxJBViRWe4oX8lQ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,1859.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 29 L 0 0 L 520 0 L 520 58 L 0 58 L 0 29 Z"/><path d="M 0 29 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 50 C 520 50 520 58 512 58 L 8 58 C 8 58 0 58 0 50 L 0 29 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 29 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 58 C 524 58 524 62 520 62 L 0 62 C 0 62 -4 62 -4 58 L -4 29 Z" fill="none"/><foreignObject width="500" height="44" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>在成功的概率为p的伯努利试验中，若以<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>ζ</mi><mo>~</mo></mover><mo>=</mo><mi>ζ</mi><mo>−</mo><mi>r</mi></mrow><annotation encoding="application/x-tex">\tilde{\zeta}=\zeta-r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1257em;vertical-align:-0.1944em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9313em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span><span style="top:-3.6134em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span></span>记等待第r次成功出现时所经历过的失败的次数，则<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>ζ</mi><mo>~</mo></mover></mrow><annotation encoding="application/x-tex">\tilde{\zeta}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1257em;vertical-align:-0.1944em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9313em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span><span style="top:-3.6134em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span></span></span></span></span>是随机变量，其概率分布亦为帕斯卡分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,29)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="_XZIIyyAK3w0IwDMXptZL" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,1847.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 652 0 L 652 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 644 0 C 644 0 652 0 652 8 L 652 29 C 652 29 652 37 644 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 652 -4 C 652 -4 656 -4 656 0 L 656 37 C 656 37 656 41 652 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="632" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="632px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 632px; max-width: 632px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mover accent="true"><mi>ζ</mi><mo>~</mo></mover><mo>=</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>ζ</mi><mo>=</mo><mi>r</mi><mo>+</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow><mi>r</mi><mo>+</mo><mi>l</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msup><mi>p</mi><mi>r</mi></msup><msup><mi>q</mi><mrow><mi>r</mi><mo>+</mo><mi>l</mi><mo>−</mo><mi>r</mi></mrow></msup><mo>=</mo><msubsup><mi>C</mi><mrow><mi>r</mi><mo>+</mo><mi>l</mi><mo>−</mo><mn>1</mn></mrow><mi>l</mi></msubsup><msup><mi>p</mi><mi>r</mi></msup><msup><mi>q</mi><mi>l</mi></msup><mo>=</mo><msubsup><mi>C</mi><mrow><mo>−</mo><mi>r</mi></mrow><mi>l</mi></msubsup><msup><mi>p</mi><mi>r</mi></msup><mo stretchy="false">(</mo><mo>−</mo><mi>q</mi><msup><mo stretchy="false">)</mo><mi>l</mi></msup><mo separator="true">,</mo><mi>l</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(\tilde{\zeta} = l) = P(\zeta = r+l) = C_{r+l-1}^{r-1} p^r q^{r+l-r} = C_{r+l-1}^{l} p^r q^l = C_{-r}^{l} p^r (-q)^l, l = 0,1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1813em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9313em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span><span style="top:-3.6134em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2139em;vertical-align:-0.3596em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.3987em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3596em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1905em;vertical-align:-0.3414em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.4169em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3414em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1544em;vertical-align:-0.3053em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3053em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="WykCJa8J136C6mtAb0fHz" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1942,1894.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 17.5 L 0 0 L 263 0 L 263 35 L 0 35 L 0 17.5 Z"/><path d="M 0 17.5 L 0 8 C 0 8 0 0 8 0 L 255 0 C 255 0 263 0 263 8 L 263 27 C 263 27 263 35 255 35 L 8 35 C 8 35 0 35 0 27 L 0 17.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 17.5 L -4 0 C -4 0 -4 -4 0 -4 L 263 -4 C 263 -4 267 -4 267 0 L 267 35 C 267 35 267 39 263 39 L 0 39 C 0 39 -4 39 -4 35 L -4 17.5 Z" fill="none"/><foreignObject width="243" height="21" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>ζ</mi><mo>~</mo></mover><mo>=</mo><msub><mover accent="true"><mi>η</mi><mo>~</mo></mover><mn>1</mn></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mover accent="true"><mi>η</mi><mo>~</mo></mover><mi>r</mi></msub><mtext>，</mtext><msub><mover accent="true"><mi>η</mi><mo>~</mo></mover><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\tilde{\zeta} = \tilde{\eta}_1 +  \dots + \tilde{\eta}_r，\tilde{\eta}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1257em;vertical-align:-0.1944em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9313em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span><span style="top:-3.6134em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8623em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1944em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1944em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">，</span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1944em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span>服从几何分布</p></div></foreignObject></g><g data-node-id="R7dkarimgGjRfV4PVfqhC" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2624,1836)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 552 0 L 552 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 544 0 C 544 0 552 0 552 8 L 552 28 C 552 28 552 36 544 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 552 -4 C 552 -4 556 -4 556 0 L 556 36 C 556 36 556 40 552 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="532" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="532px" data-formula="true" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 532px; max-width: 532px;"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>r</mi></mrow><mi mathvariant="normal">∞</mi></msubsup><msubsup><mi>C</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msup><mi>p</mi><mi>r</mi></msup><msup><mi>q</mi><mrow><mi>k</mi><mo>−</mo><mi>r</mi></mrow></msup><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>l</mi><mo>=</mo><mn>0</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><msubsup><mi>C</mi><mrow><mo>−</mo><mi>r</mi></mrow><mi>l</mi></msubsup><msup><mi>p</mi><mi>r</mi></msup><mo stretchy="false">(</mo><mo>−</mo><mi>q</mi><msup><mo stretchy="false">)</mo><mi>l</mi></msup><mo>=</mo><msup><mi>p</mi><mi>r</mi></msup><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>q</mi><msup><mo stretchy="false">)</mo><mrow><mo>−</mo><mi>r</mi></mrow></msup><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\sum_{k = r}^{\infty} C_{k-1}^{r-1} p^r q^{k-r} = \sum_{l=0}^{\infty} C_{-r}^{l} p^r (-q)^l = p^r (1-q)^{-r} = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2139em;vertical-align:-0.3596em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.3987em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3596em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1544em;vertical-align:-0.3053em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3053em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0213em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7713em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span>，两种定义都成立</p></div></foreignObject></g><g data-node-id="9sm8ll8DbVcuBXGz0NhVa" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,1965.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 90 0 L 90 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 82 0 C 82 0 90 0 90 8 L 90 23 C 90 23 90 31 82 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 90 -4 C 90 -4 94 -4 94 0 L 94 31 C 94 31 94 35 90 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="70" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>负二项分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,99,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Vl6_vQWyba2o9t8M9b9ua" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1382,1962.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 546 0 L 546 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 538 0 C 538 0 546 0 546 8 L 546 28 C 546 28 546 36 538 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 546 -4 C 546 -4 550 -4 550 0 L 550 36 C 550 36 550 40 546 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="526" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="526px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 526px; max-width: 526px;"><p>对于任意实数<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">r &gt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，称<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi><mi>b</mi><mo stretchy="false">(</mo><mi>l</mi><mo separator="true">;</mo><mi>r</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow><mo>−</mo><mi>r</mi></mrow><mi>l</mi></msubsup><msup><mi>p</mi><mi>r</mi></msup><mo stretchy="false">(</mo><mo>−</mo><mi>q</mi><msup><mo stretchy="false">)</mo><mi>l</mi></msup><mo separator="true">,</mo><mi>l</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">Nb(l;r,p) =  C_{-r}^{l} p^r (-q)^l, l = 0,1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1544em;vertical-align:-0.3053em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3053em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span>为负二项分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,555,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="SQJLJVyDa2h01RN5-YQLn" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1968,1939.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 294 0 L 294 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 286 0 C 286 0 294 0 294 8 L 294 29 C 294 29 294 37 286 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 294 -4 C 294 -4 298 -4 298 0 L 298 37 C 298 37 298 41 294 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="274" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mover accent="true"><mi>ζ</mi><mo>~</mo></mover><mo>=</mo><mi>l</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow><mo>−</mo><mi>r</mi></mrow><mi>l</mi></msubsup><msup><mi>p</mi><mi>r</mi></msup><mo stretchy="false">(</mo><mo>−</mo><mi>q</mi><msup><mo stretchy="false">)</mo><mi>l</mi></msup><mo separator="true">,</mo><mi>l</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(\tilde{\zeta} = l) =C_{-r}^{l} p^r (-q)^l, l = 0,1,2,\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1813em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9313em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span><span style="top:-3.6134em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1544em;vertical-align:-0.3053em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.453em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3053em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">−</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,303,18.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="OYKu1PqFodJlG8XF_rL3v" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2302,1939.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18.5 L 0 0 L 112 0 L 112 37 L 0 37 L 0 18.5 Z"/><path d="M 0 18.5 L 0 8 C 0 8 0 0 8 0 L 104 0 C 104 0 112 0 112 8 L 112 29 C 112 29 112 37 104 37 L 8 37 C 8 37 0 37 0 29 L 0 18.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18.5 L -4 0 C -4 0 -4 -4 0 -4 L 112 -4 C 112 -4 116 -4 116 0 L 116 37 C 116 37 116 41 112 41 L 0 41 C 0 41 -4 41 -4 37 L -4 18.5 Z" fill="none"/><foreignObject width="92" height="23" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>ζ</mi><mo>~</mo></mover><mo>∼</mo><mi>N</mi><mi>b</mi><mo stretchy="false">(</mo><mi>r</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tilde\zeta \sim Nb(r,p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1257em;vertical-align:-0.1944em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9313em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span><span style="top:-3.6134em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1667em;"><span class="mord">~</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="7I2zDCN2eZCVcEtLlfNB3" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1968,1986.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 312 0 L 312 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 304 0 C 304 0 312 0 312 8 L 312 28 C 312 28 312 36 304 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 312 -4 C 312 -4 316 -4 316 0 L 316 36 C 316 36 316 40 312 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="292" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ζ</mi><mo>=</mo><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msup><mi>p</mi><mi>r</mi></msup><msup><mi>q</mi><mrow><mi>k</mi><mo>−</mo><mi>r</mi></mrow></msup><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mi>r</mi><mo separator="true">,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo></mrow><annotation encoding="application/x-tex">P(\zeta = k) = C_{k-1}^{r-1} p^r q^{k-r}, k = r, r+1, \dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2139em;vertical-align:-0.3596em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8542em;"><span style="top:-2.3987em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1031em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3596em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,321,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="nrayqMjxZPZEhAqKhoIbg" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2320,1986.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 111 0 L 111 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 103 0 C 103 0 111 0 111 8 L 111 28 C 111 28 111 36 103 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 111 -4 C 111 -4 115 -4 115 0 L 115 36 C 115 36 115 40 111 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="91" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ζ</mi><mo>∼</mo><mi>N</mi><mi>b</mi><mo stretchy="false">(</mo><mi>r</mi><mo separator="true">,</mo><mi>p</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\zeta \sim Nb(r,p)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mord mathnormal">b</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="CKE6e7esWV288Cy8NSPtS" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2597,357)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>满足</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="bSVnn8DKis2S11yFcAmKM" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2685,334)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>非负性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="yzmQJu5gLeitABzkBBNOx" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2787,331.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 89 0 L 89 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 81 0 C 81 0 89 0 89 8 L 89 28 C 89 28 89 36 81 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 89 -4 C 89 -4 93 -4 93 0 L 93 36 C 93 36 93 40 89 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="69" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>≥</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">p(x_i) \geq 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="rUqZ437n9W-cWRaQQWvMG" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2685,380)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 62 0 L 62 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 54 0 C 54 0 62 0 62 8 L 62 23 C 62 23 62 31 54 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 62 -4 C 62 -4 66 -4 66 0 L 66 31 C 66 31 66 35 62 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="42" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>正则性</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,71,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="4xDaddaKhc7vT92OTcGj8" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2787,377.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 130 0 L 130 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 122 0 C 122 0 130 0 130 8 L 130 28 C 130 28 130 36 122 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 130 -4 C 130 -4 134 -4 134 0 L 134 36 C 134 36 134 40 130 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="110" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">∞</mi></msubsup><mi>p</mi><mo stretchy="false">(</mo><msub><mi>x</mi><mi>i</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\sum_{i=1}^{\infty} p(x_i) = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="RdaiBbD40jJEF3LsE5qyb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,894,2674.7)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 160 0 L 160 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 152 0 C 152 0 160 0 160 8 L 160 23 C 160 23 160 31 152 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 160 -4 C 160 -4 164 -4 164 0 L 164 31 C 164 31 164 35 160 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="140" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>连续型随机变量的分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,169,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="T6Vh84gucTy77q3pAGzys" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,2079.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 188 0 L 188 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 180 0 C 180 0 188 0 188 8 L 188 23 C 188 23 188 31 180 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 188 -4 C 188 -4 192 -4 192 0 L 192 31 C 192 31 192 35 188 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="168" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>密度函数（概率密度函数）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,197,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="TGaQx8RryMMp5lOzXAA7w" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1322,2032.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 497 0 L 497 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 489 0 C 489 0 497 0 497 8 L 497 28 C 497 28 497 36 489 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 497 -4 C 497 -4 501 -4 501 0 L 501 36 C 501 36 501 40 497 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="477" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>存在可积函数p(x)，使<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mrow><mo>−</mo><mi mathvariant="normal">∞</mi></mrow><mi>x</mi></msubsup><mi>p</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">F(x) = \int_{-\infty}^{x} p(t) \,dt</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2734em;vertical-align:-0.4142em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">∞</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4142em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span></span>，称p(x)为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>的（分布）密度函数</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,506,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="p0cuMoW1udSoPwraQpYYQ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1859,2032.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 115 0 L 115 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 107 0 C 107 0 115 0 115 8 L 115 28 C 115 28 115 36 107 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 115 -4 C 115 -4 119 -4 119 0 L 119 36 C 119 36 119 40 115 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="95" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>F</mi><mo mathvariant="normal" lspace="0em" rspace="0em">′</mo></msup><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x) = F'(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0019em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="NUEiYZul2Ky7E8HAWCK_b" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1322,2119.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 19 L 0 0 L 629 0 L 629 38 L 0 38 L 0 19 Z"/><path d="M 0 19 L 0 8 C 0 8 0 0 8 0 L 621 0 C 621 0 629 0 629 8 L 629 30 C 629 30 629 38 621 38 L 8 38 C 8 38 0 38 0 30 L 0 19 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 19 L -4 0 C -4 0 -4 -4 0 -4 L 629 -4 C 629 -4 633 -4 633 0 L 633 38 C 633 38 633 42 629 42 L 0 42 C 0 42 -4 42 -4 38 L -4 19 Z" fill="none"/><foreignObject width="609" height="24" x="0" y="0" class="text-obj formula-text" maxwidth="609px" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text" style="width: 609px; max-width: 609px;"><p>密度函数不是概率，但在p(x)的连续点x处，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>≈</mo><msubsup><mo>∫</mo><mi>x</mi><mrow><mi>x</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow></msubsup><mi>p</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>t</mi><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>x</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x) \Delta x \approx \int_{x}^{x+\Delta x} p(t) \,dt = F(x + \Delta x) - F(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mord">Δ</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3921em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0362em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">Δ</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,638,19)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="Jv3RvNreQSQNciZtVRrup" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1991,2078.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 402 0 L 402 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 394 0 C 394 0 402 0 402 8 L 402 23 C 402 23 402 31 394 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 402 -4 C 402 -4 406 -4 406 0 L 406 31 C 406 31 406 35 402 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="382" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>密度函数p(x)的数值反映了随机变量取x的邻近值的概率的大小</p></div></foreignObject></g><g data-node-id="BDJDR_Nf-IWmWaHx4oOyT" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1991,2119.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 19 L 0 0 L 487 0 L 487 38 L 0 38 L 0 19 Z"/><path d="M 0 19 L 0 8 C 0 8 0 0 8 0 L 479 0 C 479 0 487 0 487 8 L 487 30 C 487 30 487 38 479 38 L 8 38 C 8 38 0 38 0 30 L 0 19 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 19 L -4 0 C -4 0 -4 -4 0 -4 L 487 -4 C 487 -4 491 -4 491 0 L 491 38 C 491 38 491 42 487 42 L 0 42 C 0 42 -4 42 -4 38 L -4 19 Z" fill="none"/><foreignObject width="467" height="24" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>当<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>→</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta x \to 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Δ</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>时，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>≈</mo><msubsup><mo>∫</mo><mi>x</mi><mrow><mi>x</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow></msubsup><mi>p</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>t</mi><mo>=</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>x</mi><mo stretchy="false">)</mo><mo>−</mo><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>→</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">p(x) \Delta x \approx \int_{x}^{x+\Delta x} p(t) \,dt = F(x + \Delta x) - F(x) \to 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mord">Δ</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3921em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0362em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="mbin mtight">+</span><span class="mord mtight">Δ</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">Δ</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="-GuKsanB3BCRKAVZM_eMq" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1991,2167.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 381 0 L 381 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 373 0 C 373 0 381 0 381 8 L 381 23 C 381 23 381 31 373 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 381 -4 C 381 -4 385 -4 385 0 L 385 31 C 385 31 385 35 381 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="361" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>密度函数p(x)虽然不是概率，但其图像下方的面积等于概率</p></div></foreignObject></g><g data-node-id="h1hdPI-KSZmNfF7UtJBfi" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,2210.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 188 0 L 188 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 180 0 C 180 0 188 0 188 8 L 188 23 C 188 23 188 31 180 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 188 -4 C 188 -4 192 -4 192 0 L 192 31 C 192 31 192 35 188 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="168" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>分布函数（累积概率函数）</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,197,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="O4ULnYoNQS-JST9b4tCBQ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1322,2208.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 248 0 L 248 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 240 0 C 240 0 248 0 248 8 L 248 28 C 248 28 248 36 240 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 248 -4 C 248 -4 252 -4 252 0 L 252 36 C 252 36 252 40 248 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="228" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mrow><mo>−</mo><mi mathvariant="normal">∞</mi></mrow><mi>x</mi></msubsup><mi>p</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>t</mi><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>≤</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">F(x) = \int_{-\infty}^{x} p(t) \,dt = P(\xi \leq x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2734em;vertical-align:-0.4142em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">∞</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4142em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">x</span><span class="mclose">)</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,257,18)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="bsKcB3ebYLVwiKBEfi1e7" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1610,2210.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 104 0 L 104 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 96 0 C 96 0 104 0 104 8 L 104 23 C 104 23 104 31 96 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 104 -4 C 104 -4 108 -4 108 0 L 108 31 C 108 31 108 35 104 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="84" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>绝对连续函数</p></div></foreignObject></g><g data-node-id="kAwST5AerKLXBxBHsNNBa" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,2281.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 238 0 L 238 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 230 0 C 230 0 238 0 238 8 L 238 23 C 238 23 238 31 230 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 238 -4 C 238 -4 242 -4 242 0 L 242 31 C 242 31 242 35 238 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="218" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>连续型随机变量取个别值的概率为0</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,247,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="OpY1qN-k_qD8lsYIgK5eb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1372,2254.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 19 L 0 0 L 368 0 L 368 38 L 0 38 L 0 19 Z"/><path d="M 0 19 L 0 8 C 0 8 0 0 8 0 L 360 0 C 360 0 368 0 368 8 L 368 30 C 368 30 368 38 360 38 L 8 38 C 8 38 0 38 0 30 L 0 19 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 19 L -4 0 C -4 0 -4 -4 0 -4 L 368 -4 C 368 -4 372 -4 372 0 L 372 38 C 372 38 372 42 368 42 L 0 42 C 0 42 -4 42 -4 38 L -4 19 Z" fill="none"/><foreignObject width="348" height="24" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>对于<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>P</mi><mo stretchy="false">(</mo><mi>c</mi><mo>&lt;</mo><mi>ξ</mi><mo>≤</mo><mi>c</mi><mo>+</mo><mi>h</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mo>∫</mo><mi>c</mi><mrow><mi>c</mi><mo>+</mo><mi>h</mi></mrow></msubsup><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">p(\xi = c) \leq P(c &lt; \xi \leq c+h) = \int_{c}^{c+h} p(x) \,dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3998em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.044em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="PHF9XAEOJMtAUo7howcSW" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1372,2302.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 19 L 0 0 L 309 0 L 309 38 L 0 38 L 0 19 Z"/><path d="M 0 19 L 0 8 C 0 8 0 0 8 0 L 301 0 C 301 0 309 0 309 8 L 309 30 C 309 30 309 38 301 38 L 8 38 C 8 38 0 38 0 30 L 0 19 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 19 L -4 0 C -4 0 -4 -4 0 -4 L 309 -4 C 309 -4 313 -4 313 0 L 313 38 C 313 38 313 42 309 42 L 0 42 C 0 42 -4 42 -4 38 L -4 19 Z" fill="none"/><foreignObject width="289" height="24" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>p</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><mi>c</mi><mo stretchy="false">)</mo><mo>≤</mo><mi>l</mi><mi>i</mi><msub><mi>m</mi><mrow><mi>h</mi><mo>→</mo><mn>0</mn></mrow></msub><msubsup><mo>∫</mo><mi>c</mi><mrow><mi>c</mi><mo>+</mo><mi>h</mi></mrow></msubsup><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>d</mi><mi>x</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">0 \leq p(\xi = c) \leq lim_{h \to 0} \int_{c}^{c+h} p(x) \,dx = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7804em;vertical-align:-0.136em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3998em;vertical-align:-0.3558em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="mrel mtight">→</span><span class="mord mtight">0</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.044em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight">h</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,318,19)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="PfCp0RLZXdOs21wmNX1Gm" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1721,2303.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 116 0 L 116 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 108 0 C 108 0 116 0 116 8 L 116 28 C 116 28 116 36 108 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 116 -4 C 116 -4 120 -4 120 0 L 120 36 C 120 36 120 40 116 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="96" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>ξ</mi><mo>=</mo><mi>c</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">P(\xi = c) = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="iejk_bVoOG4ZhBywH9iRb" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1867,2281)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 48 0 L 48 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 40 0 C 40 0 48 0 48 8 L 48 23 C 48 23 48 31 40 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 48 -4 C 48 -4 52 -4 52 0 L 52 31 C 52 31 52 35 48 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="28" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>说明</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#DE6555" transform="matrix(1,0,0,1,57,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="6DrF581-_sWI3-riafOKA" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1955,2260.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 336 0 L 336 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 328 0 C 328 0 336 0 336 8 L 336 23 C 336 23 336 31 328 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 336 -4 C 336 -4 340 -4 340 0 L 340 31 C 340 31 340 35 336 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="316" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一个事件的概率为0，这个事件不一定是不可能事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,345,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="oxSp3UIxw2k1CVAOSy4i_" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2331,2260.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 294 0 L 294 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 286 0 C 286 0 294 0 294 8 L 294 23 C 294 23 294 31 286 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 294 -4 C 294 -4 298 -4 298 0 L 298 31 C 298 31 298 35 294 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="274" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一个事件是不可能事件，这个事件的概率为0</p></div></foreignObject></g><g data-node-id="06wOqhMemN5NtdDSMPoPp" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1955,2301.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 322 0 L 322 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 314 0 C 314 0 322 0 322 8 L 322 23 C 322 23 322 31 314 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 322 -4 C 322 -4 326 -4 326 0 L 326 31 C 326 31 326 35 322 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="302" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一个事件的概率为1，这个事件不一定是必然事件</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,331,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="4Xg-mRsZ8qkrGmjiPwU1G" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2317,2301.5)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 280 0 L 280 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 272 0 C 272 0 280 0 280 8 L 280 23 C 280 23 280 31 272 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 280 -4 C 280 -4 284 -4 284 0 L 284 31 C 284 31 284 35 280 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="260" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>一个事件是必然事件，这个事件的概率为1</p></div></foreignObject></g><g data-node-id="dhxoyv2zdMCtQsoxxOJFW" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1094,3270.1)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 118 0 L 118 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 110 0 C 110 0 118 0 118 8 L 118 23 C 118 23 118 31 110 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 118 -4 C 118 -4 122 -4 122 0 L 122 31 C 122 31 122 35 118 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="98" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px; font-weight: bold;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><strong>常见连续型分布</strong></p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,127,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="2ZWJ6CLKy4DNz5GnpIg8a" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,2425.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>均匀分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="h_4sDR6bHi00_c-cYGJUu" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,2414.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 520 0 L 520 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 45 C 520 45 520 53 512 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 53 C 524 53 524 57 520 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="500" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>若a,b为有限数，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>取[a,b]任意区域的概率与这个区域的测度成正比，其取区间内的任意点的可能性一样，其服从的分布称为[a,b]上的均匀分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,26.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="LJGIuKLjK7gshR_sOVYJZ" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,2350.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 37.5 L 0 0 L 231 0 L 231 75 L 0 75 L 0 37.5 Z"/><path d="M 0 37.5 L 0 8 C 0 8 0 0 8 0 L 223 0 C 223 0 231 0 231 8 L 231 67 C 231 67 231 75 223 75 L 8 75 C 8 75 0 75 0 67 L 0 37.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 37.5 L -4 0 C -4 0 -4 -4 0 -4 L 231 -4 C 231 -4 235 -4 235 0 L 235 75 C 235 75 235 79 231 79 L 0 79 C 0 79 -4 79 -4 75 L -4 37.5 Z" fill="none"/><foreignObject width="211" height="61" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>b</mi><mo>−</mo><mi>a</mi></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mi>a</mi><mo>≤</mo><mi>x</mi><mo>≤</mo><mi>b</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mi>o</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>r</mi><mi>s</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">p(x) = \begin{cases}

\dfrac{1}{b-a} &amp;, a \leq x \leq b \\

0 &amp;, others

\end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3.6em;vertical-align:-1.55em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05em;"><span style="top:-2.5em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.492em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.016em" style="width:0.8889em" viewBox="0 0 888.89 16" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"/></svg></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.016em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.016em" style="width:0.8889em" viewBox="0 0 888.89 16" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V16 H384z M384 0 H504 V16 H384z"/></svg></span></span><span style="top:-4.3em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0154em;"><span style="top:-4.0154em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.2381em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5154em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0154em;"><span style="top:-4.0154em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">b</span></span></span><span style="top:-2.2381em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">ers</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.5154em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="IdptfZCUmZJ2YA1bveToG" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,2435.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 48.5 L 0 0 L 238 0 L 238 97 L 0 97 L 0 48.5 Z"/><path d="M 0 48.5 L 0 8 C 0 8 0 0 8 0 L 230 0 C 230 0 238 0 238 8 L 238 89 C 238 89 238 97 230 97 L 8 97 C 8 97 0 97 0 89 L 0 48.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 48.5 L -4 0 C -4 0 -4 -4 0 -4 L 238 -4 C 238 -4 242 -4 242 0 L 242 97 C 242 97 242 101 238 101 L 0 101 C 0 101 -4 101 -4 97 L -4 48.5 Z" fill="none"/><foreignObject width="218" height="83" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mi>x</mi><mo>≤</mo><mi>a</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>x</mi><mo>−</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>−</mo><mi>a</mi></mrow></mfrac></mstyle></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mi>a</mi><mo>&lt;</mo><mi>x</mi><mo>≤</mo><mi>b</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo separator="true">,</mo><mi>x</mi><mo>&gt;</mo><mi>b</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">F(x) = \begin{cases}

0 &amp;, x \leq a \\

\dfrac{x-a}{b-a} &amp;, a &lt; x \leq b \\

1 &amp;, x &gt; b

\end{cases}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:4.9097em;vertical-align:-2.2048em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.65em;"><span style="top:-1.9em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-1.892em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.616em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.616em" style="width:0.8889em" viewBox="0 0 888.89 616" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V616 H384z M384 0 H504 V616 H384z"/></svg></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.616em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.616em" style="width:0.8889em" viewBox="0 0 888.89 616" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V616 H384z M384 0 H504 V616 H384z"/></svg></span></span><span style="top:-4.9em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7048em;"><span style="top:-4.9572em;"><span class="pstrut" style="height:3.2603em;"></span><span class="mord"><span class="mord">0</span></span></span><span style="top:-3.2648em;"><span class="pstrut" style="height:3.2603em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-1.4875em;"><span class="pstrut" style="height:3.2603em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.2048em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7048em;"><span style="top:-4.9572em;"><span class="pstrut" style="height:3.2603em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-3.2648em;"><span class="pstrut" style="height:3.2603em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">b</span></span></span><span style="top:-1.4875em;"><span class="pstrut" style="height:3.2603em;"></span><span class="mord"><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.2048em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p></div></foreignObject></g><g data-node-id="RPzhXbcan4rCDbefDJ8Dj" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,2196,2423)"><g fill="#FFF7D3" stroke="#FFCAA2" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 18 L 0 0 L 97 0 L 97 36 L 0 36 L 0 18 Z"/><path d="M 0 18 L 0 8 C 0 8 0 0 8 0 L 89 0 C 89 0 97 0 97 8 L 97 28 C 97 28 97 36 89 36 L 8 36 C 8 36 0 36 0 28 L 0 18 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 18 L -4 0 C -4 0 -4 -4 0 -4 L 97 -4 C 97 -4 101 -4 101 0 L 101 36 C 101 36 101 40 97 40 L 0 40 C 0 40 -4 40 -4 36 L -4 18 Z" fill="none"/><foreignObject width="77" height="22" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(187, 101, 69); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi><mo>∼</mo><mi>U</mi><mo stretchy="false">[</mo><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\xi \sim U[a,b]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="mopen">[</span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mclose">]</span></span></span></span></span></p></div></foreignObject></g><g data-node-id="XoNIWtxbjO03u2uvybYMU" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1252,2778.8)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 15.5 L 0 0 L 76 0 L 76 31 L 0 31 L 0 15.5 Z"/><path d="M 0 15.5 L 0 8 C 0 8 0 0 8 0 L 68 0 C 68 0 76 0 76 8 L 76 23 C 76 23 76 31 68 31 L 8 31 C 8 31 0 31 0 23 L 0 15.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 15.5 L -4 0 C -4 0 -4 -4 0 -4 L 76 -4 C 76 -4 80 -4 80 0 L 80 31 C 80 31 80 35 76 35 L 0 35 C 0 35 -4 35 -4 31 L -4 15.5 Z" fill="none"/><foreignObject width="56" height="17" x="0" y="0" class="text-obj" maxwidth="" data-formula="" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>正态分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,85,15.5)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="KG3trPL1pjmZGw54RGkRo" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1368,2609.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 37 L 0 0 L 520 0 L 520 74 L 0 74 L 0 37 Z"/><path d="M 0 37 L 0 8 C 0 8 0 0 8 0 L 512 0 C 512 0 520 0 520 8 L 520 66 C 520 66 520 74 512 74 L 8 74 C 8 74 0 74 0 66 L 0 37 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 37 L -4 0 C -4 0 -4 -4 0 -4 L 520 -4 C 520 -4 524 -4 524 0 L 524 74 C 524 74 524 78 520 78 L 0 78 C 0 78 -4 78 -4 74 L -4 37 Z" fill="none"/><foreignObject width="500" height="60" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p>随机变量<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></span>的密度函数为<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>π</mi></mrow></msqrt><mi>σ</mi></mrow></mfrac></mstyle><msup><mi>e</mi><mrow><mo>−</mo><mfrac><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mi>μ</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mn>2</mn><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfrac></mrow></msup><mo separator="true">,</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mi>σ</mi><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">p(x) = \dfrac{1}{\sqrt{2 \pi} \sigma} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}, -\infty &lt; x &lt; +\infty, \sigma &gt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2591em;vertical-align:-0.93em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2028em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702&#10;c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14&#10;c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54&#10;c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10&#10;s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429&#10;c69,-144,104.5,-217.7,106.5,-221&#10;l0 -0&#10;c5.3,-9.3,12,-14,20,-14&#10;H400000v40H845.2724&#10;s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7&#10;c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z&#10;M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3291em;"><span style="top:-3.4534em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.251em;"><span style="top:-2.5062em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9384em;"><span style="top:-2.9384em;margin-right:0.1em;"><span class="pstrut" style="height:2.6444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.5021em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">x</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">μ</span><span class="mclose mtight"><span class="mclose mtight">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0484em;"><span style="top:-3.0484em;margin-right:0.1em;"><span class="pstrut" style="height:2.6444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4938em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mord">∞</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord">+</span><span class="mord">∞</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">μ</span></span></span></span></span>与<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>为常数，则称其服从正态分布</p></div></foreignObject><g class="zx-node-exp" data-interact="node-expand" stroke="#E68A83" transform="matrix(1,0,0,1,529,37)"><path d="M -15 0 L -15 -20 L 15 -20 L 15 20 L -15 20 L -15 0 Z" fill="transparent" stroke="none"/><path class="zx-exp-outline" d="M -7 0 A 7 7 0, 1, 0 0 -7 A 7 7 0, 0, 0 -7 0 Z" stroke-width="1"/><path d="M -7 0 L 7 0 Z" style="pointer-events: none;"/><text text-anchor="middle" font-weight="bold" font-size="12px" y="4" fill="#333" stroke="none" style="pointer-events: none; display: none;"/></g></g><g data-node-id="1HvLL8EKzLdz3zZUjoMqA" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,2542.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 437 0 L 437 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 429 0 C 429 0 437 0 437 8 L 437 45 C 437 45 437 53 429 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 437 -4 C 437 -4 441 -4 441 0 L 441 53 C 441 53 441 57 437 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="417" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>π</mi></mrow></msqrt><mi>σ</mi></mrow></mfrac></mstyle><msup><mi>e</mi><mrow><mo>−</mo><mfrac><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>−</mo><mi>μ</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mn>2</mn><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfrac></mrow></msup><mo separator="true">,</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo separator="true">,</mo><mi>σ</mi><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">p(x) = \dfrac{1}{\sqrt{2 \pi} \sigma} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}, -\infty &lt; x &lt; +\infty, \sigma &gt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2591em;vertical-align:-0.93em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2028em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702&#10;c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14&#10;c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54&#10;c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10&#10;s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429&#10;c69,-144,104.5,-217.7,106.5,-221&#10;l0 -0&#10;c5.3,-9.3,12,-14,20,-14&#10;H400000v40H845.2724&#10;s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7&#10;c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z&#10;M834 80h400000v40h-400000z"/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1328em;"><span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3291em;"><span style="top:-3.4534em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.251em;"><span style="top:-2.5062em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9384em;"><span style="top:-2.9384em;margin-right:0.1em;"><span class="pstrut" style="height:2.6444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.5021em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">x</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight">μ</span><span class="mclose mtight"><span class="mclose mtight">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0484em;"><span style="top:-3.0484em;margin-right:0.1em;"><span class="pstrut" style="height:2.6444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4938em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">−</span><span class="mord">∞</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord">+</span><span class="mord">∞</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span>，<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">μ</span></span></span></span></span>与<span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></span>为常数</p></div></foreignObject></g><g data-node-id="G3Nv70Tix6rucx2yhpT7J" class="zx-node" data-interact="node" transform="matrix(1,0,0,1,1928,2605.3)"><g fill="transparent" stroke="none" stroke-width="3" stroke-dasharray="" transform="matrix(1,0,0,1,0,0)"><path fill="transparent" stroke="none" stroke-width="0" d="M 0 26.5 L 0 0 L 359 0 L 359 53 L 0 53 L 0 26.5 Z"/><path d="M 0 26.5 L 0 8 C 0 8 0 0 8 0 L 351 0 C 351 0 359 0 359 8 L 359 45 C 359 45 359 53 351 53 L 8 53 C 8 53 0 53 0 45 L 0 26.5 Z"/></g><path class="zx-node-hover" stroke="#5EC8F8" d="M -4 26.5 L -4 0 C -4 0 -4 -4 0 -4 L 359 -4 C 359 -4 363 -4 363 0 L 363 53 C 363 53 363 57 359 57 L 0 57 C 0 57 -4 57 -4 53 L -4 26.5 Z" fill="none"/><foreignObject width="339" height="39" x="0" y="0" class="text-obj formula-text" maxwidth="" data-formula="true" style="color: rgb(114, 41, 13); font-family: 微软雅黑, &quot;Microsoft YaHei&quot;; font-size: 14px;" transform="matrix(1,0,0,1,10,7)"><div xmlns="http://www.w3.org/1999/xhtml" class="n-text"><p><span><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><msqrt><mrow><mn>2</mn><mi>π</mi></mrow></msqrt><mi>σ</mi></mrow></mfrac></mstyle><msubsup><mo>∫</mo><mrow><mo>−</mo><mi mathvariant="normal">∞</mi></mrow><mi>x</mi></msubsup><msup><mi>e</mi><mrow><mo>−</mo><mfrac><mrow><mo stretchy="false">(</mo><mi>t</mi><mo>−</mo><mi>μ</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mrow><mn>2</mn><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfrac></mrow></msup><mtext> </mtext><mi>d</mi><mi>x</mi><mo separator="true">,</mo><mo>−</mo><mi mathvariant="normal">∞</mi><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mo>+</mo><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">F(x) = \dfrac{1}{\sqrt{2 \pi} \sigma} \int_{-\infty}^{x} e^{-\frac{(t-\mu)^2}{2 \sigma^2}} \,dx, -\infty &lt; x &lt; +\infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2591em;vertical-align:-0.93em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2028em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9072em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span><span style="top:-2.8672em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path 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style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.93em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">∞</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4142em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3291em;"><span style="top:-3.4534em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.251em;"><span style="top:-2.5062em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9384em;"><span style="top:-2.9384em;margin-right:0.1em;"><span class="pstrut" style="height:2.6444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span><span style="top:-3.2255em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.5021em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="m