数理统计基础.svg

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<text x="4731.0" y="208" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="23" font-weight="900" fill="#0F172A">检验</text>
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<text x="178" y="401.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="32" font-weight="900" fill="#0F172A">第1章 统计推断的地基</text>
<text x="178" y="431.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="19" font-weight="700" fill="#334155">先把“样本、统计量、模型、似然”这些对象摆正</text>
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<text x="1504.0" y="500.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">总体与样本</text>
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<text x="2288.0" y="500.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">统计量合法性</text>
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286.883 -0.220 285.761 -0.220 Q 283.929 -0.220 282.775 1.243 Q 281.625 2.709 281.625 5.093 Q 281.625 7.478 282.775 8.941 Q 283.929 10.403 285.761 10.403 Q 286.883 10.403 287.681 9.964 Q 288.482 9.527 289.005 8.626 Z M 283.342 5.093 Q 283.342 3.261 284.096 2.217 Q 284.851 1.174 286.169 1.174 Q 287.487 1.174 288.245 2.217 Q 289.005 3.261 289.005 5.093 Q 289.005 6.926 288.245 7.969 Q 287.487 9.013 286.169 9.013 Q 284.851 9.013 284.096 7.969 Q 283.342 6.926 283.342 5.093 Z" transform="translate(2257.21 549.63) scale(1 -1)" fill="#111827"/>
<text x="2258.0" y="593.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">若 μ,σ² 未知： </text>
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<text x="2258.0" y="637.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">若 a,b 已知： </text>
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<text x="2258.0" y="670.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">常见坑：题中“未知”两个字决定是否合法</text>
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<rect x="3025.0" y="464.0" width="760.0" height="320.5" rx="9" fill="#93C5FD" opacity="0.22"/>
<rect x="3020.0" y="458.0" width="760.0" height="320.5" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="3020.0" y="458.0" width="760.0" height="9" rx="9" fill="#3B82F6"/>
<rect x="3020.0" y="466.0" width="760.0" height="9" fill="#3B82F6" opacity="0.20"/>
<circle cx="3045.0" cy="493.0" r="16" fill="#DBEAFE" stroke="#3B82F6" stroke-width="2.4"/>
<text x="3045.0" y="499.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#1D4ED8" text-anchor="middle">3</text>
<text x="3072.0" y="500.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">样本均值与方差</text>
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<text x="3738.0" y="499.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#1D4ED8" text-anchor="middle">公式</text>
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<text x="3856.0" y="500.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">平方和恒等式</text>
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<text x="4610.0" y="740.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">矩估计就是用 Ak 替换总体矩 μk(θ)</text>
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<rect x="1452.0" y="804.5" width="760.0" height="260.4" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
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<rect x="1452.0" y="812.5" width="760.0" height="9" fill="#3B82F6" opacity="0.20"/>
<circle cx="1477.0" cy="839.5" r="16" fill="#DBEAFE" stroke="#3B82F6" stroke-width="2.4"/>
<text x="1477.0" y="845.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#1D4ED8" text-anchor="middle">6</text>
<text x="1504.0" y="846.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">经验分布函数</text>
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<text x="2170.0" y="845.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#1D4ED8" text-anchor="middle">公式</text>
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<text x="2288.0" y="846.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">似然函数</text>
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<text x="2258.0" y="1064.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">支持集含 θ 时，指标函数不能丢</text>
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<text x="3072.0" y="846.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">指数型分布族</text>
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<text x="3042.0" y="1060.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Bernoulli/Poisson/指数/正态都可套这个结构</text>
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<text x="3829.0" y="845.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#1D4ED8" text-anchor="middle">9</text>
<text x="3856.0" y="846.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">常见模型矩</text>
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<text x="4522.0" y="845.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#1D4ED8" text-anchor="middle">速查</text>
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<text x="178" y="1212.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="32" font-weight="900" fill="#0F172A">第2章 抽样分布工具箱</text>
<text x="178" y="1242.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="19" font-weight="700" fill="#334155">所有区间和检验都在这里找“统计量的分布”</text>
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<text x="1112.0" y="1311.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">正态线性组合</text>
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<text x="1082.0" y="1505.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">这是构造 Z 统计量的入口</text>
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<rect x="1849.0" y="1275.9" width="760.0" height="248.7" rx="9" fill="#6EE7B7" opacity="0.22"/>
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<circle cx="1869.0" cy="1304.9" r="16" fill="#D1FAE5" stroke="#10B981" stroke-width="2.4"/>
<text x="1869.0" y="1310.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#047857" text-anchor="middle">12</text>
<text x="1896.0" y="1311.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">单正态样本分布</text>
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<text x="1866.0" y="1489.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">x̄ 与 S² 相互独立</text>
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<text x="2650.0" y="1469.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">若用 Sn： </text>
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122.010 5.857 Q 122.958 6.562 123.767 6.872 Q 124.577 7.184 125.453 7.184 Q 126.447 7.184 127.774 6.652 Q 127.872 6.606 127.918 6.588 Q 127.973 6.571 128.109 6.516 Q 129.508 5.964 130.358 5.964 Q 131.133 5.964 131.896 6.302 Q 132.662 6.643 133.590 7.409 Z M 146.977 10.138 L 146.726 8.846 L 143.410 8.846 L 142.335 3.354 Q 142.280 3.047 142.254 2.839 Q 142.228 2.631 142.228 2.515 Q 142.228 1.937 142.575 1.674 Q 142.922 1.411 143.691 1.411 L 145.370 1.411 L 145.090 0.021 L 143.500 0.021 Q 142.020 0.021 141.292 0.599 Q 140.566 1.177 140.566 2.351 Q 140.566 2.559 140.592 2.807 Q 140.618 3.056 140.673 3.354 L 141.748 8.846 L 140.338 8.846 L 140.601 10.138 L 141.982 10.138 L 142.543 13.011 L 144.205 13.011 L 143.653 10.138 L 146.977 10.138 Z M 152.144 14.058 Q 150.936 11.982 150.346 9.947 Q 149.759 7.915 149.759 5.828 Q 149.759 3.744 150.352 1.697 Q 150.944 -0.349 152.144 -2.419 L 150.699 -2.419 Q 149.346 -0.294 148.672 1.755 Q 147.999 3.805 147.999 5.828 Q 147.999 7.843 148.667 9.884 Q 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201.314 -2.419 Q 202.514 -0.349 203.106 1.697 Q 203.699 3.744 203.699 5.828 Q 203.699 7.915 203.106 9.947 Q 202.514 11.982 201.314 14.058 Z M 0.000 3.498 L 0.000 4.654 L 57.425 4.654 L 57.425 3.498 L 0.000 3.498 Z M 77.165 22.107 L 77.165 23.264 L 116.446 23.264 L 116.446 22.107 L 77.165 22.107 Z M 79.477 3.462 L 79.477 4.619 L 111.821 4.619 L 111.821 3.462 L 79.477 3.462 Z" transform="translate(2736.08 1470.53) scale(1 -1)" fill="#111827"/>
<text x="2650.0" y="1509.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">自测题常考这个转换</text>
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<text x="3437.0" y="1310.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#047857" text-anchor="middle">14</text>
<text x="3464.0" y="1311.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">平方和分解</text>
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<text x="4130.0" y="1310.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#047857" text-anchor="middle">公式</text>
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<text x="3434.0" y="1424.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">两项除以 σ² 后独立</text>
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<text x="4248.0" y="1311.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">两个正态总体</text>
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<text x="2288.0" y="1629.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">F 分布</text>
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<text x="3072.0" y="1629.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">上侧分位数</text>
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<text x="3856.0" y="1629.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">次序统计量</text>
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<text x="4522.0" y="1628.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#047857" text-anchor="middle">定义</text>
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<text x="3826.0" y="1713.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">连续总体 F,f</text>
<text x="3826.0" y="1749.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">联合密度： </text>
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2.550 L 146.394 0.905 L 134.814 5.105 L 134.814 6.605 L 146.394 10.805 L 146.394 9.160 Z M 160.252 2.350 L 162.166 2.350 L 162.166 0.055 L 160.252 0.055 L 160.252 2.350 Z M 166.404 2.350 L 168.329 2.350 L 168.329 0.055 L 166.404 0.055 L 166.404 2.350 Z M 154.093 2.350 L 156.015 2.350 L 156.015 0.055 L 154.093 0.055 L 154.093 2.350 Z M 187.603 9.160 L 178.281 5.845 L 187.603 2.550 L 187.603 0.905 L 176.023 5.105 L 176.023 6.605 L 187.603 10.805 L 187.603 9.160 Z M 204.272 10.172 L 199.626 5.212 L 202.474 0.055 L 200.566 0.055 L 198.427 4.067 L 194.704 0.055 L 192.689 0.055 L 197.667 5.385 L 195.022 10.172 L 196.927 10.172 L 198.869 6.513 L 202.257 10.172 L 204.272 10.172 Z M 214.425 6.163 L 213.240 0.055 L 211.569 0.055 L 212.754 6.099 Q 212.835 6.524 212.878 6.848 Q 212.925 7.175 212.925 7.362 Q 212.925 8.123 212.445 8.545 Q 211.968 8.970 211.109 8.970 Q 209.771 8.970 208.806 8.079 Q 207.840 7.192 207.539 5.666 L 206.429 0.055 L 204.767 0.055 L 206.727 10.172 L 208.389 10.172 L 208.057 8.582 Q 208.751 9.458 209.725 9.935 Q 210.702 10.415 211.777 10.415 Q 213.115 10.415 213.850 9.692 Q 214.587 8.970 214.587 7.660 Q 214.587 7.336 214.546 6.966 Q 214.506 6.596 214.425 6.163 Z" transform="translate(3920.56 1749.91) scale(1 -1)" fill="#111827"/>
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<text x="4640.0" y="1629.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">单个次序统计量</text>
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11.901 Q 268.460 12.130 268.460 12.261 Q 268.460 12.794 268.125 13.089 Q 267.791 13.386 267.190 13.386 Q 266.253 13.386 265.577 12.763 Q 264.901 12.142 264.691 11.074 L 263.914 7.146 L 262.750 7.146 L 264.122 14.228 L 265.286 14.228 L 265.053 13.115 Q 265.539 13.728 266.220 14.062 Q 266.904 14.398 267.657 14.398 Q 268.594 14.398 269.108 13.892 Q 269.624 13.386 269.624 12.470 Q 269.624 12.243 269.596 11.984 Q 269.567 11.725 269.511 11.422 Z M 274.397 11.743 L 282.503 11.743 L 282.503 10.669 L 274.397 10.669 L 274.397 11.743 Z M 288.277 14.228 L 289.440 14.228 L 288.044 7.019 L 288.036 6.988 Q 287.803 5.780 287.500 5.331 Q 287.215 4.908 286.666 4.682 Q 286.120 4.453 285.375 4.453 L 284.938 4.453 L 285.128 5.438 L 285.426 5.438 Q 286.108 5.438 286.397 5.724 Q 286.685 6.007 286.881 7.019 L 288.277 14.228 Z M 288.821 16.986 L 289.985 16.986 L 289.699 15.511 L 288.536 15.511 L 288.821 16.986 Z" transform="translate(4609.50 1772.54) scale(1 -1)" fill="#111827"/>
<text x="4610.0" y="1823.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">本质：二项计数达到 k</text>
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<text x="1477.0" y="1919.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#047857" text-anchor="middle">22</text>
<text x="1504.0" y="1920.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">最大最小</text>
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<text x="2170.0" y="1919.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#047857" text-anchor="middle">公式</text>
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5.934 Q 162.855 3.910 162.181 1.861 Q 161.508 -0.188 160.155 -2.313 L 158.710 -2.313 Q 159.909 -0.243 160.502 1.803 Q 161.095 3.850 161.095 5.934 Q 161.095 8.021 160.502 10.053 Q 159.909 12.088 158.710 14.163 Z" transform="translate(1472.75 2081.19) scale(1 -1)" fill="#111827"/>
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<text x="2288.0" y="1920.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">两个次序统计量</text>
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3.925 277.344 1.876 Q 276.671 -0.173 275.318 -2.298 L 273.872 -2.298 Q 275.072 -0.228 275.665 1.818 Q 276.257 3.865 276.257 5.949 Q 276.257 8.036 275.665 10.068 Q 275.072 12.103 273.872 14.179 Z" transform="translate(2257.35 2086.82) scale(1 -1)" fill="#111827"/>
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<text x="3072.0" y="1920.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">Uniform特例</text>
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169.408 15.761 Q 168.807 15.761 168.139 15.552 Q 167.473 15.344 166.714 14.919 L 166.714 16.210 Q 167.485 16.519 168.155 16.677 Q 168.827 16.835 169.383 16.835 Q 170.850 16.835 171.722 16.100 Q 172.594 15.368 172.594 14.142 Q 172.594 13.559 172.376 13.037 Q 172.159 12.517 171.583 11.809 Q 171.425 11.625 170.577 10.748 Q 169.731 9.872 168.187 8.298 Z M 180.183 14.179 Q 178.974 12.103 178.385 10.068 Q 177.798 8.036 177.798 5.949 Q 177.798 3.865 178.390 1.818 Q 178.983 -0.228 180.183 -2.298 L 178.737 -2.298 Q 177.385 -0.173 176.711 1.876 Q 176.038 3.925 176.038 5.949 Q 176.038 7.964 176.705 10.004 Q 177.376 12.048 178.737 14.179 L 180.183 14.179 Z M 183.960 1.677 L 186.941 1.677 L 186.941 11.967 L 183.697 11.317 L 183.697 12.979 L 186.923 13.629 L 188.747 13.629 L 188.747 1.677 L 191.727 1.677 L 191.727 0.142 L 183.960 0.142 L 183.960 1.677 Z M 199.000 6.709 L 210.579 6.709 L 210.579 5.174 L 199.000 5.174 L 199.000 6.709 Z M 224.392 8.724 Q 224.140 8.860 223.814 8.932 Q 223.490 9.004 223.120 9.004 Q 221.790 9.004 220.796 7.995 Q 219.804 6.990 219.478 5.299 L 218.457 0.142 L 216.795 0.142 L 218.773 10.259 L 220.435 10.259 L 220.120 8.686 Q 220.779 9.562 221.695 10.030 Q 222.614 10.502 223.652 10.502 Q 223.924 10.502 224.184 10.470 Q 224.447 10.441 224.710 10.369 L 224.392 8.724 Z M 225.234 14.179 L 226.679 14.179 Q 228.032 12.048 228.705 10.004 Q 229.379 7.964 229.379 5.949 Q 229.379 3.925 228.705 1.876 Q 228.032 -0.173 226.679 -2.298 L 225.234 -2.298 Q 226.433 -0.228 227.026 1.818 Q 227.619 3.865 227.619 5.949 Q 227.619 8.036 227.026 10.068 Q 226.433 12.103 225.234 14.179 Z" transform="translate(3040.75 2083.28) scale(1 -1)" fill="#111827"/>
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<text x="3856.0" y="1920.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">极限分布</text>
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<text x="3826.0" y="1972.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">大数定律： </text>
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186.207 3.472 185.010 1.677 Q 183.814 -0.116 181.545 -0.116 Q 179.278 -0.116 178.082 1.677 Q 176.885 3.472 176.885 6.877 Q 176.885 10.291 178.082 12.083 Q 179.278 13.878 181.545 13.878 Z M 189.603 2.443 L 191.508 2.443 L 191.508 0.887 L 190.028 -2.003 L 188.863 -2.003 L 189.603 0.887 L 189.603 2.443 Z M 199.215 1.682 L 202.196 1.682 L 202.196 11.973 L 198.952 11.323 L 198.952 12.985 L 202.178 13.635 L 204.002 13.635 L 204.002 1.682 L 206.982 1.682 L 206.982 0.147 L 199.215 0.147 L 199.215 1.682 Z M 210.173 14.184 L 211.619 14.184 Q 212.971 12.054 213.645 10.010 Q 214.319 7.969 214.319 5.955 Q 214.319 3.931 213.645 1.882 Q 212.971 -0.168 211.619 -2.292 L 210.173 -2.292 Q 211.373 -0.223 211.966 1.824 Q 212.558 3.871 212.558 5.955 Q 212.558 8.042 211.966 10.074 Q 211.373 12.109 210.173 14.184 Z M 74.239 20.605 L 74.239 21.414 L 85.684 21.414 L 85.684 20.605 L 74.239 20.605 Z M 65.988 3.625 L 65.988 4.781 L 129.587 4.781 L 129.587 3.625 L 65.988 3.625 Z" transform="translate(3824.96 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<text x="3826.0" y="2050.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">样本矩 Ak → E(Xᵏ)</text>
<text x="3826.0" y="2082.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">经验频率 → 概率</text>
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<text x="4640.0" y="1920.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">Slutsky</text>
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<text x="1504.0" y="2184.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">Delta法</text>
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<text x="1474.0" y="2339.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">函数估计量渐近正态性的主工具</text>
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<text x="2288.0" y="2184.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">比例近似</text>
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<text x="2258.0" y="2323.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">检验标准误常用 p0</text>
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<text x="3072.0" y="2184.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">充分统计量定义</text>
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<text x="3042.0" y="2233.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">给定 T 后样本条件分布不含 θ</text>
<text x="3042.0" y="2265.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">T 压缩样本且不损失关于 θ 的信息</text>
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<text x="3042.0" y="2329.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">T 的一一变换仍充分</text>
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<text x="3856.0" y="2184.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">因子分解定理</text>
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Q 281.765 2.902 281.765 4.385 L 281.765 10.120 L 283.428 10.120 L 283.428 0.003 L 281.765 0.003 L 281.765 1.558 Q 281.161 0.636 280.361 0.188 Q 279.563 -0.260 278.505 -0.260 Q 276.762 -0.260 275.857 0.824 Q 274.955 1.908 274.955 3.995 Z M 279.138 10.363 L 279.138 10.363 Z M 291.973 14.060 L 291.973 12.675 L 290.383 12.675 Q 289.490 12.675 289.140 12.314 Q 288.793 11.953 288.793 11.013 L 288.793 10.120 L 291.531 10.120 L 291.531 8.828 L 288.793 8.828 L 288.793 0.003 L 287.122 0.003 L 287.122 8.828 L 285.533 8.828 L 285.533 10.120 L 287.122 10.120 L 287.122 10.825 Q 287.122 12.514 287.909 13.285 Q 288.695 14.060 290.400 14.060 L 291.973 14.060 Z M 298.486 14.060 L 298.486 12.675 L 296.896 12.675 Q 296.003 12.675 295.653 12.314 Q 295.306 11.953 295.306 11.013 L 295.306 10.120 L 298.044 10.120 L 298.044 8.828 L 295.306 8.828 L 295.306 0.003 L 293.635 0.003 L 293.635 8.828 L 292.046 8.828 L 292.046 10.120 L 293.635 10.120 L 293.635 10.825 Q 293.635 12.514 294.422 13.285 Q 295.208 14.060 296.913 14.060 L 298.486 14.060 Z M 299.877 10.120 L 301.539 10.120 L 301.539 0.003 L 299.877 0.003 L 299.877 10.120 Z M 299.877 14.060 L 301.539 14.060 L 301.539 11.953 L 299.877 11.953 L 299.877 14.060 Z M 312.298 9.733 L 312.298 8.178 Q 311.593 8.568 310.884 8.761 Q 310.176 8.955 309.454 8.955 Q 307.835 8.955 306.939 7.929 Q 306.046 6.906 306.046 5.053 Q 306.046 3.200 306.939 2.174 Q 307.835 1.150 309.454 1.150 Q 310.176 1.150 310.884 1.344 Q 311.593 1.538 312.298 1.928 L 312.298 0.390 Q 311.601 0.066 310.856 -0.095 Q 310.113 -0.260 309.272 -0.260 Q 306.985 -0.260 305.638 1.176 Q 304.294 2.613 304.294 5.053 Q 304.294 7.527 305.652 8.944 Q 307.014 10.363 309.381 10.363 Q 310.147 10.363 310.879 10.204 Q 311.610 10.048 312.298 9.733 Z M 315.188 10.120 L 316.850 10.120 L 316.850 0.003 L 315.188 0.003 L 315.188 10.120 Z M 315.188 14.060 L 316.850 14.060 L 316.850 11.953 L 315.188 11.953 L 315.188 14.060 Z M 328.982 5.478 L 328.982 4.665 L 321.340 4.665 Q 321.449 2.948 322.374 2.049 Q 323.299 1.150 324.953 1.150 Q 325.910 1.150 326.809 1.385 Q 327.708 1.619 328.595 2.090 L 328.595 0.517 Q 327.699 0.139 326.759 -0.061 Q 325.820 -0.260 324.855 -0.260 Q 322.432 -0.260 321.019 1.148 Q 319.605 2.558 319.605 4.963 Q 319.605 7.446 320.946 8.903 Q 322.288 10.363 324.565 10.363 Q 326.606 10.363 327.794 9.048 Q 328.982 7.735 328.982 5.478 Z M 327.320 5.966 Q 327.303 7.328 326.557 8.140 Q 325.811 8.955 324.583 8.955 Q 323.192 8.955 322.357 8.169 Q 321.522 7.383 321.394 5.955 L 327.320 5.966 Z M 340.121 6.111 L 340.121 0.003 L 338.459 0.003 L 338.459 6.056 Q 338.459 7.492 337.898 8.204 Q 337.338 8.918 336.219 8.918 Q 334.872 8.918 334.094 8.059 Q 333.317 7.203 333.317 5.721 L 333.317 0.003 L 331.646 0.003 L 331.646 10.120 L 333.317 10.120 L 333.317 8.548 Q 333.915 9.461 334.722 9.912 Q 335.531 10.363 336.589 10.363 Q 338.332 10.363 339.225 9.285 Q 340.121 8.206 340.121 6.111 Z M 345.080 12.993 L 345.080 10.120 L 348.502 10.120 L 348.502 8.828 L 345.080 8.828 L 345.080 3.336 Q 345.080 2.099 345.418 1.746 Q 345.756 1.393 346.797 1.393 L 348.502 1.393 L 348.502 0.003 L 346.797 0.003 Q 344.871 0.003 344.140 0.720 Q 343.409 1.440 343.409 3.336 L 343.409 8.828 L 342.189 8.828 L 342.189 10.120 L 343.409 10.120 L 343.409 12.993 L 345.080 12.993 Z" transform="translate(3826.05 2233.22) scale(1 -1)" fill="#111827"/>
<text x="3826.0" y="2267.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">离散型也可看 Pθ(X=x | T=t)</text>
<text x="3826.0" y="2299.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">含 θ 的支持约束要归入 gθ(T)</text>
<text x="3826.0" y="2331.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">指数族可直接读出充分统计量</text>
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<rect x="4588.0" y="2142.1" width="760.0" height="282.4" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="4588.0" y="2142.1" width="760.0" height="9" rx="9" fill="#10B981"/>
<rect x="4588.0" y="2150.1" width="760.0" height="9" fill="#10B981" opacity="0.20"/>
<circle cx="4613.0" cy="2177.1" r="16" fill="#D1FAE5" stroke="#10B981" stroke-width="2.4"/>
<text x="4613.0" y="2183.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#047857" text-anchor="middle">31</text>
<text x="4640.0" y="2184.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">常见充分统计量</text>
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<text x="5306.0" y="2183.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#047857" text-anchor="middle">速查</text>
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305.570 -2.396 Q 306.770 -0.327 307.363 1.720 Q 307.955 3.766 307.955 5.851 Q 307.955 7.938 307.363 9.970 Q 306.770 12.005 305.570 14.080 Z" transform="translate(4608.92 2392.81) scale(1 -1)" fill="#111827"/>
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<text x="178" y="2543.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="32" font-weight="900" fill="#0F172A">第3章 点估计工坊</text>
<text x="178" y="2573.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="19" font-weight="700" fill="#334155">MOM 看矩，MLE 看似然，评价看 Bias / MSE / C-R</text>
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<text x="6607.0" y="2551.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="800" fill="#B45309" text-anchor="middle">17 张公式卡</text>
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<text x="1112.0" y="2642.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">点估计对象</text>
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<text x="1778.0" y="2641.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B45309" text-anchor="middle">定义</text>
<text x="1082.0" y="2691.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">用统计量 T(X) 估计 g(θ)</text>
<text x="1082.0" y="2723.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">估计值是 T(x1,…,xn)</text>
<text x="1082.0" y="2755.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">估计量不能含未知参数</text>
<text x="1082.0" y="2787.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">函数参数也可直接估 g(θ)</text>
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<text x="1869.0" y="2641.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#B45309" text-anchor="middle">33</text>
<text x="1896.0" y="2642.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">Bias / MSE</text>
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187.540 0.700 Q 186.425 -0.121 184.473 -0.121 Q 183.661 -0.121 182.779 0.038 Q 181.898 0.197 180.924 0.512 L 180.924 2.229 Q 181.846 1.749 182.739 1.509 Q 183.632 1.272 184.511 1.272 Q 185.685 1.272 186.315 1.674 Q 186.948 2.075 186.948 2.807 Q 186.948 3.483 186.491 3.845 Q 186.037 4.206 184.491 4.541 L 183.913 4.677 Q 182.369 5.001 181.681 5.674 Q 180.996 6.348 180.996 7.521 Q 180.996 8.949 182.008 9.724 Q 183.019 10.502 184.881 10.502 Q 185.800 10.502 186.612 10.366 Q 187.428 10.233 188.113 9.961 Z M 192.221 8.298 L 196.679 8.298 L 196.679 7.224 L 190.685 7.224 L 190.685 8.298 Q 191.412 9.051 192.666 10.318 Q 193.923 11.586 194.244 11.954 Q 194.857 12.642 195.100 13.120 Q 195.345 13.598 195.345 14.059 Q 195.345 14.812 194.817 15.285 Q 194.289 15.761 193.441 15.761 Q 192.840 15.761 192.172 15.552 Q 191.507 15.344 190.748 14.919 L 190.748 16.210 Q 191.519 16.519 192.189 16.677 Q 192.860 16.835 193.417 16.835 Q 194.884 16.835 195.756 16.100 Q 196.628 15.368 196.628 14.142 Q 196.628 13.559 196.409 13.037 Q 196.193 12.517 195.616 11.809 Q 195.458 11.625 194.611 10.748 Q 193.765 9.872 192.221 8.298 Z" transform="translate(1864.18 2764.93) scale(1 -1)" fill="#111827"/>
<text x="1866.0" y="2798.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">无偏时 MSE=Var</text>
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<text x="2680.0" y="2642.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">无偏与相合</text>
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<text x="3434.0" y="2805.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">无偏估计之间比方差</text>
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<text x="4248.0" y="2642.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">矩法一般式</text>
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<text x="4218.0" y="2815.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">多参数需要同数量矩方程</text>
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<text x="1866.0" y="3080.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">代入 μ̂=A1，v̂=A2−A1²</text>
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<text x="2680.0" y="2912.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">MLE定义</text>
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9.964 Q 110.615 10.415 111.728 10.415 Q 113.280 10.415 114.138 9.397 Q 114.997 8.383 114.997 6.550 Q 114.997 5.050 114.462 3.691 Q 113.930 2.333 112.927 1.257 Q 112.259 0.543 111.418 0.168 Q 110.580 -0.208 109.649 -0.208 Q 108.574 -0.208 107.843 0.240 Q 107.111 0.688 106.750 1.573 L 105.709 -3.792 L 104.047 -3.792 L 106.767 10.172 L 108.429 10.172 L 108.132 8.637 Z M 121.740 1.510 L 117.717 1.510 Q 117.446 -0.382 117.723 -1.183 Q 118.071 -2.171 119.014 -2.171 Q 119.961 -2.171 120.683 -1.177 Q 121.315 -0.305 121.740 1.510 Z M 121.934 2.584 Q 122.106 4.381 121.883 5.012 Q 121.537 6.012 120.606 6.012 Q 119.639 6.012 118.931 5.024 Q 118.375 4.229 117.938 2.584 L 121.934 2.584 Z M 120.791 6.961 Q 122.308 6.961 122.915 5.619 Q 123.522 4.286 123.061 1.921 Q 122.606 -0.439 121.472 -1.778 Q 120.347 -3.126 118.830 -3.126 Q 117.306 -3.126 116.705 -1.778 Q 116.104 -0.439 116.560 1.921 Q 117.021 4.286 118.140 5.619 Q 119.267 6.961 120.791 6.961 Z M 130.009 14.092 Q 128.801 12.016 128.211 9.981 Q 127.624 7.949 127.624 5.862 Q 127.624 3.778 128.217 1.731 Q 128.810 -0.315 130.009 -2.385 L 128.564 -2.385 Q 127.211 -0.260 126.538 1.789 Q 125.864 3.839 125.864 5.862 Q 125.864 7.877 126.532 9.918 Q 127.202 11.961 128.564 14.092 L 130.009 14.092 Z M 142.595 10.172 L 137.949 5.212 L 140.797 0.055 L 138.889 0.055 L 136.750 4.067 L 133.027 0.055 L 131.012 0.055 L 135.990 5.385 L 133.345 10.172 L 135.250 10.172 L 137.192 6.513 L 140.580 10.172 L 142.595 10.172 Z M 144.811 6.860 L 145.975 6.860 L 145.690 5.385 L 144.526 5.385 L 144.811 6.860 Z M 144.279 4.102 L 145.443 4.102 L 144.059 -2.980 L 142.895 -2.980 L 144.279 4.102 Z M 148.027 14.092 L 149.472 14.092 Q 150.825 11.961 151.498 9.918 Q 152.172 7.877 152.172 5.862 Q 152.172 3.839 151.498 1.789 Q 150.825 -0.260 149.472 -2.385 L 148.027 -2.385 Q 149.226 -0.315 149.819 1.731 Q 150.411 3.778 150.411 5.862 Q 150.411 7.949 149.819 9.981 Q 149.226 12.016 148.027 14.092 Z" transform="translate(2650.25 3060.29) scale(1 -1)" fill="#111827"/>
<text x="2650.0" y="3108.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">MLE 可不唯一</text>
<circle cx="3366.0" cy="3117.6" r="5" fill="#F59E0B" opacity="0.62"/>
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<rect x="3412.0" y="2870.5" width="760.0" height="225.7" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="3412.0" y="2870.5" width="760.0" height="9" rx="9" fill="#F59E0B"/>
<rect x="3412.0" y="2878.5" width="760.0" height="9" fill="#F59E0B" opacity="0.20"/>
<circle cx="3437.0" cy="2905.5" r="16" fill="#FEF3C7" stroke="#F59E0B" stroke-width="2.4"/>
<text x="3437.0" y="2911.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#B45309" text-anchor="middle">41</text>
<text x="3464.0" y="2912.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">MLE步骤</text>
<rect x="4102.0" y="2892.5" width="56.0" height="28" rx="14" fill="#FEF3C7" stroke="#F59E0B" stroke-width="1.4"/>
<text x="4130.0" y="2911.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B45309" text-anchor="middle">MLE</text>
<text x="3434.0" y="2961.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">写参数空间 Θ</text>
<text x="3434.0" y="2993.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">写 L 和支持约束</text>
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<text x="3434.0" y="3067.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">最后比较边界与可行域</text>
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<rect x="4201.0" y="2876.5" width="760.0" height="224.8" rx="9" fill="#FCD34D" opacity="0.22"/>
<rect x="4196.0" y="2870.5" width="760.0" height="224.8" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="4196.0" y="2870.5" width="760.0" height="9" rx="9" fill="#F59E0B"/>
<rect x="4196.0" y="2878.5" width="760.0" height="9" fill="#F59E0B" opacity="0.20"/>
<circle cx="4221.0" cy="2905.5" r="16" fill="#FEF3C7" stroke="#F59E0B" stroke-width="2.4"/>
<text x="4221.0" y="2911.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#B45309" text-anchor="middle">42</text>
<text x="4248.0" y="2912.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">MLE不变性</text>
<rect x="4886.0" y="2892.5" width="56.0" height="28" rx="14" fill="#FEF3C7" stroke="#F59E0B" stroke-width="1.4"/>
<text x="4914.0" y="2911.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B45309" text-anchor="middle">MLE</text>
<text x="4218.0" y="2961.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">若 θ̂ 是 θ 的 MLE</text>
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<text x="4218.0" y="3034.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">可用于 θ²、1/λ、P(X&gt;c)</text>
<text x="4218.0" y="3066.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">多值 MLE 时函数值也可能多值</text>
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<rect x="4985.0" y="2876.5" width="760.0" height="240.6" rx="9" fill="#FCD34D" opacity="0.22"/>
<rect x="4980.0" y="2870.5" width="760.0" height="240.6" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="4980.0" y="2870.5" width="760.0" height="9" rx="9" fill="#F59E0B"/>
<rect x="4980.0" y="2878.5" width="760.0" height="9" fill="#F59E0B" opacity="0.20"/>
<circle cx="5005.0" cy="2905.5" r="16" fill="#FEF3C7" stroke="#F59E0B" stroke-width="2.4"/>
<text x="5005.0" y="2911.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#B45309" text-anchor="middle">43</text>
<text x="5032.0" y="2912.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">常见MLE</text>
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<text x="5698.0" y="2911.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B45309" text-anchor="middle">MLE</text>
<text x="5002.0" y="2964.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Bernoulli： </text>
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<text x="2258.0" y="3381.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">支持依赖 θ 时常非正则</text>
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<text x="3072.0" y="3205.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">C-R不等式</text>
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<text x="3738.0" y="3204.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B45309" text-anchor="middle">C-R</text>
<text x="3042.0" y="3254.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">T 无偏估 g(θ)</text>
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<text x="3042.0" y="3377.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">达到下界 ⇒ 有效估计</text>
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<text x="3856.0" y="3205.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">常见信息量</text>
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120.763 5.472 L 120.763 0.142 L 119.092 0.142 L 119.092 10.259 L 120.763 10.259 L 120.763 8.686 Q 121.289 9.608 122.127 10.054 Q 122.968 10.502 124.171 10.502 Q 124.341 10.502 124.549 10.479 Q 124.757 10.458 125.009 10.412 L 125.018 8.707 Z M 130.753 14.179 Q 129.545 12.103 128.955 10.068 Q 128.369 8.036 128.369 5.949 Q 128.369 3.865 128.961 1.818 Q 129.554 -0.228 130.753 -2.298 L 129.308 -2.298 Q 127.955 -0.173 127.282 1.876 Q 126.608 3.925 126.608 5.949 Q 126.608 7.964 127.276 10.004 Q 127.947 12.048 129.308 14.179 L 130.753 14.179 Z M 142.272 11.857 Q 141.477 12.490 139.318 12.490 Q 137.031 12.490 136.826 11.432 Q 136.661 10.603 138.965 10.169 Q 140.772 9.834 141.639 8.822 Q 142.688 7.602 142.200 5.102 Q 141.729 2.709 140.223 1.298 Q 138.705 -0.121 136.537 -0.121 Q 134.378 -0.121 133.409 1.298 Q 132.444 2.709 132.932 5.192 Q 133.285 7.033 134.811 8.524 Q 135.407 9.103 136.147 9.429 Q 134.875 10.140 135.126 11.415 Q 135.606 13.872 139.590 13.872 Q 141.584 13.872 142.544 13.239 L 142.272 11.857 Z M 137.303 8.975 Q 136.644 8.715 136.011 8.056 Q 135.037 7.033 134.684 5.192 Q 134.323 3.359 134.892 2.327 Q 135.470 1.289 136.815 1.289 Q 138.144 1.289 139.118 2.336 Q 140.104 3.385 140.439 5.102 Q 140.781 6.900 140.130 7.767 Q 139.436 8.695 138.315 8.796 Q 137.745 8.851 137.303 8.975 Z M 145.037 14.179 L 146.483 14.179 Q 147.835 12.048 148.509 10.004 Q 149.183 7.964 149.183 5.949 Q 149.183 3.925 148.509 1.876 Q 147.835 -0.173 146.483 -2.298 L 145.037 -2.298 Q 146.237 -0.228 146.830 1.818 Q 147.422 3.865 147.422 5.949 Q 147.422 8.036 146.830 10.068 Q 146.237 12.103 145.037 14.179 Z" transform="translate(4609.86 3326.05) scale(1 -1)" fill="#111827"/>
<text x="4610.0" y="3358.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">充分统计量可以改进估计</text>
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<text x="178" y="3556.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="32" font-weight="900" fill="#0F172A">第4章 区间估计雷达</text>
<text x="178" y="3586.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="19" font-weight="700" fill="#334155">选一个分布不含未知参数的枢轴变量，然后反解参数</text>
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<text x="6607.0" y="3564.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="800" fill="#6D28D9" text-anchor="middle">18 张公式卡</text>
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<text x="1085.0" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#6D28D9" text-anchor="middle">49</text>
<text x="1112.0" y="3655.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">置信区间</text>
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<text x="1778.0" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">定义</text>
<text x="1082.0" y="3704.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">随机区间 [L(X),U(X)]</text>
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<text x="1082.0" y="3770.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">1−α：置信水平</text>
<text x="1082.0" y="3802.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">L,U：置信限；多参数为置信域</text>
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<text x="1869.0" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#6D28D9" text-anchor="middle">50</text>
<text x="1896.0" y="3655.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">枢轴变量法</text>
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<text x="2562.0" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">步骤</text>
<text x="1866.0" y="3704.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Q(X,θ) 含 θ 与样本</text>
<text x="1866.0" y="3736.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Q 的分布不含未知参数</text>
<text x="1866.0" y="3768.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">写 P(a&lt;Q&lt;b)=1−α</text>
<text x="1866.0" y="3800.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">代数反解 θ 或 g(θ)</text>
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<text x="2680.0" y="3655.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">分位数方向</text>
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<text x="3346.0" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">提醒</text>
<text x="2650.0" y="3705.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">上侧分位： </text>
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<text x="2650.0" y="3738.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">双侧常用 α/2</text>
<text x="2650.0" y="3770.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">χ²/F 不对称，端点易反</text>
<text x="2650.0" y="3802.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">反解时检查单调性</text>
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<text x="3464.0" y="3655.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">μ，σ²已知</text>
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<text x="4125.5" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">正态CI</text>
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<text x="3434.0" y="3800.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">下限： </text>
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<text x="3434.0" y="3843.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">上限： </text>
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<text x="4248.0" y="3655.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">μ，σ²未知</text>
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<text x="4909.5" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">正态CI</text>
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<text x="4218.0" y="3758.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">CI: </text>
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<text x="4218.0" y="3796.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">小样本正态必须用 t</text>
<text x="4218.0" y="3828.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">大样本可近似用 z</text>
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<text x="5032.0" y="3655.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">σ²，μ未知</text>
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<text x="5693.5" y="3654.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">正态CI</text>
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<text x="1082.0" y="4183.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">自由度 n，不是 n−1</text>
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<text x="1896.0" y="3949.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">预测区间</text>
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199.474 7.680 Q 199.087 7.680 198.702 7.373 L 198.565 7.600 L 200.427 9.031 L 200.711 9.031 L 203.291 0.657 L 203.337 0.657 L 209.018 19.360 L 209.666 19.360 Z M 213.901 1.691 L 216.881 1.691 L 216.881 11.982 L 213.638 11.331 L 213.638 12.993 L 216.864 13.644 L 218.688 13.644 L 218.688 1.691 L 221.668 1.691 L 221.668 0.156 L 213.901 0.156 L 213.901 1.691 Z M 235.491 11.756 L 235.491 6.724 L 240.520 6.724 L 240.520 5.189 L 235.491 5.189 L 235.491 0.156 L 233.973 0.156 L 233.973 5.189 L 228.940 5.189 L 228.940 6.724 L 233.973 6.724 L 233.973 11.756 L 235.491 11.756 Z M 248.381 1.691 L 251.361 1.691 L 251.361 11.982 L 248.118 11.331 L 248.118 12.993 L 251.344 13.644 L 253.168 13.644 L 253.168 1.691 L 256.148 1.691 L 256.148 0.156 L 248.381 0.156 L 248.381 1.691 Z M 262.553 13.644 L 264.088 13.644 L 259.391 -1.561 L 257.856 -1.561 L 262.553 13.644 Z M 274.397 6.264 L 273.212 0.156 L 271.541 0.156 L 272.726 6.200 Q 272.807 6.625 272.850 6.949 Q 272.897 7.276 272.897 7.464 Q 272.897 8.224 272.417 8.646 Q 271.940 9.071 271.081 9.071 Q 269.743 9.071 268.778 8.180 Q 267.812 7.293 267.511 5.767 L 266.401 0.156 L 264.739 0.156 L 266.699 10.273 L 268.361 10.273 L 268.029 8.683 Q 268.723 9.559 269.697 10.036 Q 270.674 10.516 271.749 10.516 Q 273.087 10.516 273.822 9.793 Q 274.559 9.071 274.559 7.761 Q 274.559 7.438 274.518 7.068 Q 274.478 6.698 274.397 6.264 Z M 209.294 18.038 L 209.294 19.194 L 278.127 19.194 L 278.127 18.038 L 209.294 18.038 Z" transform="translate(1866.79 4054.77) scale(1 -1)" fill="#111827"/>
<text x="1866.0" y="4087.7" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">若用 Sn 要换算</text>
<text x="1866.0" y="4119.7" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">自测题重点</text>
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<rect x="2633.0" y="3913.1" width="760.0" height="242.4" rx="9" fill="#C4B5FD" opacity="0.22"/>
<rect x="2628.0" y="3907.1" width="760.0" height="242.4" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="2628.0" y="3907.1" width="760.0" height="9" rx="9" fill="#8B5CF6"/>
<rect x="2628.0" y="3915.1" width="760.0" height="9" fill="#8B5CF6" opacity="0.20"/>
<circle cx="2653.0" cy="3942.1" r="16" fill="#EDE9FE" stroke="#8B5CF6" stroke-width="2.4"/>
<text x="2653.0" y="3948.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#6D28D9" text-anchor="middle">57</text>
<text x="2680.0" y="3949.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">均值差方差已知</text>
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<text x="3334.8" y="3948.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">两样本CI</text>
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<text x="2650.0" y="4120.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">目标若是 b−a，注意符号</text>
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<text x="3464.0" y="3949.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">均值差等方差未知</text>
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<text x="3434.0" y="4127.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">前提：正态、独立、等方差</text>
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<text x="4248.0" y="3949.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">配对区间</text>
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<text x="4902.8" y="3948.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">两样本CI</text>
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<text x="5032.0" y="3949.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">方差比区间</text>
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<text x="5002.0" y="4151.1" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">自由度顺序跟 Sx²/Sy² 一致</text>
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<text x="1112.0" y="4280.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">一般均值大样本</text>
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<text x="1082.0" y="4329.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">CLT + Slutsky</text>
<text x="1082.0" y="4367.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">CI: </text>
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<text x="1082.0" y="4404.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">非正态大样本可用</text>
<text x="1082.0" y="4436.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">小样本非正态要谨慎</text>
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<rect x="1849.0" y="4244.8" width="760.0" height="267.8" rx="9" fill="#C4B5FD" opacity="0.22"/>
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<circle cx="1869.0" cy="4273.8" r="16" fill="#EDE9FE" stroke="#8B5CF6" stroke-width="2.4"/>
<text x="1869.0" y="4279.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#6D28D9" text-anchor="middle">62</text>
<text x="1896.0" y="4280.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">比例Wald</text>
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<text x="2557.5" y="4279.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">近似CI</text>
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<text x="1866.0" y="4375.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">CI: </text>
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127.511 17.538 128.146 17.853 Q 128.781 18.169 129.560 18.169 Q 130.647 18.169 131.248 17.457 Q 131.849 16.747 131.849 15.464 Q 131.849 14.414 131.475 13.463 Q 131.102 12.511 130.400 11.759 Q 129.933 11.259 129.344 10.996 Q 128.757 10.733 128.106 10.733 Q 127.353 10.733 126.841 11.047 Q 126.329 11.360 126.076 11.979 L 125.348 8.224 L 124.184 8.224 L 126.088 17.999 L 127.252 17.999 L 127.043 16.925 Z M 133.481 20.743 L 134.493 20.743 Q 135.439 19.252 135.911 17.821 Q 136.382 16.392 136.382 14.982 Q 136.382 13.566 135.911 12.131 Q 135.439 10.696 134.493 9.209 L 133.481 9.209 Q 134.321 10.658 134.735 12.091 Q 135.150 13.523 135.150 14.982 Q 135.150 16.443 134.735 17.866 Q 134.321 19.290 133.481 20.743 Z M 115.305 -0.534 L 114.475 -4.809 L 113.306 -4.809 L 114.135 -0.578 Q 114.192 -0.281 114.222 -0.054 Q 114.255 0.174 114.255 0.306 Q 114.255 0.838 113.919 1.133 Q 113.585 1.431 112.984 1.431 Q 112.047 1.431 111.371 0.808 Q 110.695 0.186 110.485 -0.882 L 109.708 -4.809 L 108.545 -4.809 L 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<text x="1866.0" y="4422.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">保守样本量： </text>
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<text x="1866.0" y="4469.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">有预估 p0： </text>
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<text x="2680.0" y="4280.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">Wilson/Score</text>
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<text x="3341.5" y="4279.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">近似CI</text>
<text x="2650.0" y="4338.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">中心： </text>
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28.444 L 175.664 28.444 L 175.664 27.288 L 69.853 27.288 Z M 72.166 3.599 L 72.166 4.755 L 122.847 4.755 L 122.847 3.599 L 72.166 3.599 Z M 147.869 3.599 L 147.869 4.755 L 171.039 4.755 L 171.039 3.599 L 147.869 3.599 Z" transform="translate(2710.53 4393.75) scale(1 -1)" fill="#111827"/>
<text x="2650.0" y="4434.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">p 接近 0/1 时比 Wald 稳</text>
<text x="2650.0" y="4466.2" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">课件重点提到 score interval</text>
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<text x="3437.0" y="4279.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#6D28D9" text-anchor="middle">64</text>
<text x="3464.0" y="4280.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">Poisson λ</text>
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<text x="4115.8" y="4279.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">近似/精确</text>
<text x="3434.0" y="4335.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">近似： </text>
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<text x="3434.0" y="4433.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">精确： </text>
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<text x="4248.0" y="4280.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">指数率 λ</text>
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<text x="5693.5" y="4279.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#6D28D9" text-anchor="middle">精确CI</text>
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54.132 0.988 L 53.355 -2.939 L 52.191 -2.939 L 53.563 4.143 L 54.727 4.143 L 54.494 3.030 Q 54.979 3.643 55.661 3.977 Q 56.345 4.313 57.098 4.313 Q 58.035 4.313 58.549 3.807 Q 59.065 3.301 59.065 2.384 Q 59.065 2.158 59.036 1.899 Q 59.008 1.640 58.951 1.336 Z M 60.981 6.887 L 61.993 6.887 Q 62.940 5.395 63.412 3.965 Q 63.883 2.536 63.883 1.126 Q 63.883 -0.291 63.412 -1.725 Q 62.940 -3.160 61.993 -4.647 L 60.981 -4.647 Q 61.821 -3.198 62.236 -1.766 Q 62.651 -0.333 62.651 1.126 Q 62.651 2.587 62.236 4.009 Q 61.821 5.434 60.981 6.887 Z M 67.670 2.391 L 69.574 2.391 L 69.574 0.836 L 68.094 -2.055 L 66.930 -2.055 L 67.670 0.836 L 67.670 2.391 Z M 96.132 13.584 L 100.353 13.584 Q 102.194 13.584 103.160 12.725 Q 104.128 11.867 104.128 10.213 Q 104.128 7.990 102.700 6.753 Q 101.272 5.516 98.691 5.516 L 96.395 5.516 L 95.338 0.096 L 93.505 0.096 L 96.132 13.584 Z M 97.670 12.083 L 96.693 7.016 L 98.988 7.016 Q 100.541 7.016 101.370 7.811 Q 102.203 8.606 102.203 10.086 Q 102.203 11.034 101.639 11.557 Q 101.075 12.083 100.055 12.083 L 97.670 12.083 Z M 109.899 14.133 Q 108.690 12.057 108.101 10.022 Q 107.514 7.990 107.514 5.903 Q 107.514 3.819 108.106 1.773 Q 108.699 -0.274 109.899 -2.344 L 108.453 -2.344 Q 107.101 -0.219 106.427 1.830 Q 105.754 3.880 105.754 5.903 Q 105.754 7.918 106.421 9.959 Q 107.092 12.002 108.453 14.133 L 109.899 14.133 Z M 112.474 13.584 L 123.883 13.584 L 123.594 12.046 L 118.778 12.046 L 116.466 0.096 L 114.633 0.096 L 116.946 12.046 L 112.176 12.046 L 112.474 13.584 Z M 127.379 13.584 L 128.914 13.584 L 124.217 -1.621 L 122.682 -1.621 L 127.379 13.584 Z M 137.335 6.510 L 131.588 6.510 Q 131.201 3.808 131.597 2.663 Q 132.094 1.252 133.441 1.252 Q 134.794 1.252 135.826 2.672 Q 136.728 3.917 137.335 6.510 Z M 137.613 8.045 Q 137.858 10.612 137.540 11.514 Q 137.046 12.942 135.716 12.942 Q 134.335 12.942 133.323 11.531 Q 132.528 10.395 131.904 8.045 L 137.613 8.045 Z M 135.979 14.298 Q 138.147 14.298 139.014 12.381 Q 139.882 10.476 139.223 7.097 Q 138.572 3.727 136.953 1.813 Q 135.346 -0.112 133.178 -0.112 Q 131.002 -0.112 130.143 1.813 Q 129.285 3.727 129.935 7.097 Q 130.594 10.476 132.193 12.381 Q 133.803 14.298 135.979 14.298 Z M 157.377 9.274 L 148.705 6.770 L 157.377 4.296 L 157.377 2.689 L 145.797 6.013 L 145.797 7.548 L 157.377 10.864 L 157.377 9.274 Z M 145.797 1.631 L 157.377 1.631 L 157.377 0.096 L 145.797 0.096 L 145.797 1.631 Z M 164.180 4.108 L 165.365 10.213 L 167.036 10.213 L 165.851 4.169 Q 165.761 3.727 165.721 3.412 Q 165.680 3.096 165.680 2.888 Q 165.680 2.119 166.148 1.697 Q 166.620 1.278 167.478 1.278 Q 168.814 1.278 169.788 2.180 Q 170.765 3.085 171.062 4.614 L 172.175 10.213 L 173.837 10.213 L 171.878 0.096 L 170.216 0.096 L 170.548 1.686 Q 169.846 0.801 168.874 0.316 Q 167.903 -0.167 166.810 -0.167 Q 165.481 -0.167 164.741 0.561 Q 164.001 1.290 164.001 2.591 Q 164.001 2.859 164.044 3.267 Q 164.090 3.675 164.180 4.108 Z M 176.151 14.133 L 177.596 14.133 Q 178.949 12.002 179.622 9.959 Q 180.296 7.918 180.296 5.903 Q 180.296 3.880 179.622 1.830 Q 178.949 -0.219 177.596 -2.344 L 176.151 -2.344 Q 177.350 -0.274 177.943 1.773 Q 178.535 3.819 178.535 5.903 Q 178.535 7.990 177.943 10.022 Q 177.350 12.057 176.151 14.133 Z M 187.449 8.496 L 199.029 8.496 L 199.029 6.979 L 187.449 6.979 L 187.449 8.496 Z M 187.449 4.811 L 199.029 4.811 L 199.029 3.276 L 187.449 3.276 L 187.449 4.811 Z M 205.832 4.108 L 207.017 10.213 L 208.688 10.213 L 207.503 4.169 Q 207.413 3.727 207.373 3.412 Q 207.332 3.096 207.332 2.888 Q 207.332 2.119 207.801 1.697 Q 208.272 1.278 209.130 1.278 Q 210.466 1.278 211.440 2.180 Q 212.417 3.085 212.715 4.614 L 213.827 10.213 L 215.490 10.213 L 213.530 0.096 L 211.868 0.096 L 212.200 1.686 Q 211.498 0.801 210.526 0.316 Q 209.555 -0.167 208.462 -0.167 Q 207.133 -0.167 206.393 0.561 Q 205.653 1.290 205.653 2.591 Q 205.653 2.859 205.696 3.267 Q 205.742 3.675 205.832 4.108 Z M 224.362 11.454 L 223.532 7.178 L 222.363 7.178 L 223.192 11.409 Q 223.249 11.706 223.279 11.933 Q 223.312 12.162 223.312 12.293 Q 223.312 12.825 222.976 13.121 Q 222.642 13.418 222.041 13.418 Q 221.104 13.418 220.428 12.795 Q 219.752 12.174 219.542 11.105 L 218.765 7.178 L 217.601 7.178 L 218.973 14.260 L 220.137 14.260 L 219.904 13.147 Q 220.390 13.760 221.072 14.094 Q 221.756 14.430 222.508 14.430 Q 223.445 14.430 223.959 13.924 Q 224.475 13.418 224.475 12.502 Q 224.475 12.275 224.447 12.016 Q 224.418 11.757 224.362 11.454 Z" transform="translate(5001.21 4330.23) scale(1 -1)" fill="#111827"/>
<text x="5002.0" y="4364.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">取 0&lt;a&lt;b&lt;1，bⁿ−aⁿ=1−α</text>
<text x="5002.0" y="4397.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">θ CI: </text>
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<text x="5002.0" y="4432.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">常用单侧： </text>
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<text x="131" y="4669.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="26" font-weight="900" fill="#B91C1C" text-anchor="middle">5</text>
<text x="178" y="4657.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="32" font-weight="900" fill="#0F172A">第5章 假设检验法庭</text>
<text x="178" y="4687.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="19" font-weight="700" fill="#334155">H0 下统计量怎么分布，备择方向就决定拒绝域朝哪边开</text>
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<text x="6607.0" y="4665.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="800" fill="#B91C1C" text-anchor="middle">20 张公式卡</text>
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<text x="1477.0" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#B91C1C" text-anchor="middle">67</text>
<text x="1504.0" y="4756.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">假设与拒绝域</text>
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<text x="2170.0" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">定义</text>
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44.795 7.993 Q 45.041 10.559 44.723 11.461 Q 44.229 12.889 42.899 12.889 Q 41.518 12.889 40.506 11.479 Q 39.711 10.343 39.086 7.993 L 44.795 7.993 Z M 43.162 14.245 Q 45.330 14.245 46.197 12.329 Q 47.065 10.424 46.406 7.044 Q 45.755 3.674 44.136 1.760 Q 42.529 -0.165 40.361 -0.165 Q 38.185 -0.165 37.326 1.760 Q 36.468 3.674 37.118 7.044 Q 37.777 10.424 39.376 12.329 Q 40.986 14.245 43.162 14.245 Z M 54.119 5.706 Q 54.183 5.038 54.752 3.954 Q 55.420 2.700 56.683 1.995 Q 57.923 1.309 59.259 1.298 L 65.554 1.298 L 65.554 -0.139 L 59.259 -0.139 Q 57.524 -0.139 55.920 0.754 Q 54.319 1.651 53.460 3.240 Q 52.602 4.830 52.602 6.521 Q 52.602 8.192 53.460 9.782 Q 54.319 11.372 55.920 12.274 Q 57.524 13.178 59.259 13.178 L 65.554 13.178 L 65.554 11.742 L 59.259 11.742 Q 57.923 11.733 56.683 11.036 Q 55.429 10.322 54.752 9.077 Q 54.174 7.993 54.093 7.151 L 65.554 7.151 L 65.554 5.706 L 54.119 5.706 Z M 74.833 7.993 L 81.210 7.993 L 81.210 6.458 L 74.833 6.458 L 74.833 7.993 Z M 78.030 12.294 Q 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<text x="1474.0" y="4839.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">拒绝域 D ⊂ 样本空间</text>
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<text x="1474.0" y="4905.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">检验统计量 K(X) 刻画 D</text>
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<text x="2288.0" y="4756.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">两类错误与功效</text>
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<text x="2954.0" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">概念</text>
<text x="2258.0" y="4805.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">第一类错误：H0 真却拒绝</text>
<text x="2258.0" y="4837.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">第二类错误：H1 真却未拒绝</text>
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<text x="2258.0" y="4903.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">原则：先控第一类，再提高功效</text>
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<text x="3072.0" y="4756.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">检验水平</text>
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<text x="3738.0" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">公式</text>
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<text x="3042.0" y="4889.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">复合 H0 取最坏情况上确界</text>
<text x="3042.0" y="4921.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">结论不能写成“接受 H1 为真”</text>
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<rect x="3804.0" y="4714.0" width="760.0" height="224.5" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
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<rect x="3804.0" y="4722.0" width="760.0" height="9" fill="#EF4444" opacity="0.20"/>
<circle cx="3829.0" cy="4749.0" r="16" fill="#FEE2E2" stroke="#EF4444" stroke-width="2.4"/>
<text x="3829.0" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#B91C1C" text-anchor="middle">70</text>
<text x="3856.0" y="4756.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">拒绝域方向</text>
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<text x="4522.0" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">口诀</text>
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<text x="4640.0" y="4756.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">单均值 σ²已知</text>
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<text x="5305.1" y="4755.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">Z检验</text>
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<text x="1504.0" y="5021.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">单均值 σ²未知</text>
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<text x="2288.0" y="5021.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">单方差 μ未知</text>
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<text x="2258.0" y="5196.8" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">双侧取两尾 α/2</text>
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<text x="3042.0" y="5133.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">自由度 n，不是 n−1</text>
<text x="3042.0" y="5165.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">其他拒绝域同 χ² 方向</text>
<text x="3042.0" y="5197.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">方差检验强依赖正态性</text>
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<text x="3856.0" y="5021.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">已知σ的功效</text>
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<text x="3826.0" y="5144.7" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">左尾/双尾按拒绝域代入</text>
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<text x="4640.0" y="5021.4" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">两均值差方差已知</text>
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<text x="4610.0" y="5160.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">右/左/双尾按 δ 的备择方向</text>
<text x="4610.0" y="5192.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">独立正态或大样本可用</text>
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<text x="1504.0" y="5294.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">两均值差等方差未知</text>
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140.535 1.753 Q 141.407 1.020 141.407 -0.206 Q 141.407 -0.789 141.189 -1.311 Q 140.972 -1.831 140.396 -2.539 Q 140.238 -2.723 139.390 -3.599 Q 138.544 -4.475 137.000 -6.050 Z M 44.530 3.644 L 44.530 4.800 L 180.278 4.800 L 180.278 3.644 L 44.530 3.644 Z" transform="translate(1473.89 5407.27) scale(1 -1)" fill="#111827"/>
<text x="1474.0" y="5444.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">前提：正态、独立、等方差</text>
<text x="1474.0" y="5476.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">不等方差用近似 Z/Welch</text>
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<text x="2288.0" y="5294.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">配对检验</text>
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<text x="2950.1" y="5293.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">两样本</text>
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<text x="2258.0" y="5461.0" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">配对数据不能当独立两样本</text>
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<text x="3072.0" y="5294.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">方差比检验</text>
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<text x="3856.0" y="5294.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">一般均值大样本</text>
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Q 158.687 -0.168 157.334 -2.292 L 155.889 -2.292 Q 157.089 -0.223 157.681 1.824 Q 158.274 3.871 158.274 5.955 Q 158.274 8.042 157.681 10.074 Q 157.089 12.109 155.889 14.184 Z M 35.383 3.625 L 35.383 4.781 L 75.302 4.781 L 75.302 3.625 L 35.383 3.625 Z M 60.103 0.850 L 60.103 1.659 L 71.548 1.659 L 71.548 0.850 L 60.103 0.850 Z" transform="translate(3826.41 5352.51) scale(1 -1)" fill="#111827"/>
<text x="3826.0" y="5392.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">非正态大样本由 CLT 支撑</text>
<text x="3826.0" y="5424.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">小样本非正态不能直接用 t</text>
<text x="3826.0" y="5456.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">结论回到实际语境</text>
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<text x="4640.0" y="5294.6" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">单比例检验</text>
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134.913 9.082 Q 135.908 9.082 137.235 8.550 Q 137.324 8.516 137.370 8.496 Q 137.434 8.470 137.570 8.415 Q 138.969 7.865 139.819 7.865 Q 140.593 7.865 141.357 8.204 Q 142.123 8.542 143.050 9.311 Z M 151.741 13.655 L 154.198 13.655 L 157.921 2.093 L 160.179 13.655 L 161.959 13.655 L 159.329 0.168 L 156.863 0.168 L 153.151 11.802 L 150.894 0.168 L 149.113 0.168 L 151.741 13.655 Z M 168.190 14.205 Q 166.982 12.129 166.392 10.094 Q 165.805 8.062 165.805 5.975 Q 165.805 3.891 166.398 1.844 Q 166.990 -0.202 168.190 -2.272 L 166.745 -2.272 Q 165.392 -0.147 164.718 1.902 Q 164.045 3.951 164.045 5.975 Q 164.045 7.990 164.712 10.030 Q 165.383 12.074 166.745 14.205 L 168.190 14.205 Z M 175.552 12.453 Q 174.144 12.453 173.433 11.065 Q 172.725 9.681 172.725 6.897 Q 172.725 4.125 173.433 2.737 Q 174.144 1.350 175.552 1.350 Q 176.971 1.350 177.679 2.737 Q 178.391 4.125 178.391 6.897 Q 178.391 9.681 177.679 11.065 Q 176.971 12.453 175.552 12.453 Z M 175.552 13.898 Q 177.821 13.898 179.018 12.103 Q 180.215 10.311 180.215 6.897 Q 180.215 3.492 179.018 1.697 Q 177.821 -0.095 175.552 -0.095 Q 173.286 -0.095 172.089 1.697 Q 170.892 3.492 170.892 6.897 Q 170.892 10.311 172.089 12.103 Q 173.286 13.898 175.552 13.898 Z M 183.611 2.463 L 185.516 2.463 L 185.516 0.908 L 184.036 -1.983 L 182.871 -1.983 L 183.611 0.908 L 183.611 2.463 Z M 193.223 1.703 L 196.203 1.703 L 196.203 11.993 L 192.960 11.343 L 192.960 13.005 L 196.186 13.655 L 198.010 13.655 L 198.010 1.703 L 200.990 1.703 L 200.990 0.168 L 193.223 0.168 L 193.223 1.703 Z M 204.181 14.205 L 205.626 14.205 Q 206.979 12.074 207.652 10.030 Q 208.326 7.990 208.326 5.975 Q 208.326 3.951 207.652 1.902 Q 206.979 -0.147 205.626 -2.272 L 204.181 -2.272 Q 205.380 -0.202 205.973 1.844 Q 206.565 3.891 206.565 5.975 Q 206.565 8.062 205.973 10.094 Q 205.380 12.129 204.181 14.205 Z M 35.383 3.645 L 35.383 4.801 L 123.594 4.801 L 123.594 3.645 L 35.383 3.645 Z M 44.862 0.870 L 44.862 1.679 L 123.594 1.679 L 123.594 0.870 L 44.862 0.870 Z" 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<text x="4610.0" y="5431.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">检验标准误用 p0</text>
<text x="4610.0" y="5463.3" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">区间标准误常用 p̂</text>
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<text x="1504.0" y="5573.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">两比例检验</text>
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<text x="2258.0" y="5709.7" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">也可用总数 Y=ΣXi</text>
<text x="2258.0" y="5741.7" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">大样本近似依赖 nλ0 足够大</text>
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<text x="3072.0" y="5573.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">似然比检验</text>
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<text x="3738.0" y="5572.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">LRT</text>
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<text x="4640.0" y="5573.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">p值</text>
<rect x="5278.0" y="5553.9" width="56.0" height="28" rx="14" fill="#FEE2E2" stroke="#EF4444" stroke-width="1.4"/>
<text x="5306.0" y="5572.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#B91C1C" text-anchor="middle">结论</text>
<text x="4610.0" y="5622.9" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">p值：H0 下至少同样极端的概率</text>
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Q 131.907 0.580 131.530 -0.381 Q 131.154 -1.342 130.460 -2.086 Q 130.005 -2.580 129.410 -2.847 Q 128.815 -3.112 128.163 -3.112 Q 127.476 -3.112 126.970 -2.797 Q 126.464 -2.479 126.146 -1.854 L 125.938 -2.928 L 124.774 -2.928 L 126.690 6.912 L 127.854 6.912 L 127.101 3.079 Z M 139.002 3.945 L 138.781 2.845 Q 138.320 3.098 137.806 3.223 Q 137.294 3.351 136.752 3.351 Q 135.833 3.351 135.305 3.037 Q 134.779 2.725 134.779 2.187 Q 134.779 1.562 136.005 1.226 Q 136.100 1.202 136.145 1.187 L 136.517 1.074 Q 137.681 0.752 138.069 0.398 Q 138.458 0.044 138.458 -0.569 Q 138.458 -1.696 137.563 -2.404 Q 136.669 -3.112 135.220 -3.112 Q 134.658 -3.112 134.039 -3.003 Q 133.419 -2.896 132.673 -2.669 L 132.899 -1.467 Q 133.539 -1.797 134.158 -1.967 Q 134.779 -2.137 135.348 -2.137 Q 136.202 -2.137 136.736 -1.771 Q 137.270 -1.405 137.270 -0.842 Q 137.270 -0.235 135.866 0.139 L 135.746 0.170 L 135.348 0.271 Q 134.461 0.506 134.051 0.888 Q 133.640 1.270 133.640 1.865 Q 133.640 2.996 134.490 3.660 Q 135.342 4.324 136.803 4.324 Q 137.377 4.324 137.924 4.229 Q 138.472 4.136 139.002 3.945 Z M 143.665 14.245 L 143.665 -4.255 L 142.130 -4.255 L 142.130 14.245 L 143.665 14.245 Z M 147.496 14.144 L 148.941 14.144 Q 150.294 12.013 150.967 9.970 Q 151.641 7.929 151.641 5.914 Q 151.641 3.891 150.967 1.841 Q 150.294 -0.208 148.941 -2.333 L 147.496 -2.333 Q 148.695 -0.263 149.288 1.784 Q 149.880 3.830 149.880 5.914 Q 149.880 8.001 149.288 10.033 Q 148.695 12.068 147.496 14.144 Z" transform="translate(4610.05 5723.10) scale(1 -1)" fill="#111827"/>
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<text x="178" y="5909.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="32" font-weight="900" fill="#0F172A">11次作业与自测关卡</text>
<text x="178" y="5939.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="19" font-weight="700" fill="#334155">把题目类型压缩成可复用路线，不抄原题</text>
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<text x="1085.0" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">87</text>
<text x="1112.0" y="6008.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W1 基础对象</text>
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<text x="1774.1" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="1082.0" y="6057.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">有限/无限总体与分布</text>
<text x="1082.0" y="6089.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">统计量是否合法</text>
<text x="1082.0" y="6121.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">样本变换与样本方差</text>
<text x="1082.0" y="6153.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">联合密度与模型识别</text>
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<text x="1869.0" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">88</text>
<text x="1896.0" y="6008.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W2 抽样分布</text>
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<text x="2558.1" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="1866.0" y="6057.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">正态样本均值/方差</text>
<text x="1866.0" y="6089.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">χ²、t、F 构造与分位数</text>
<text x="1866.0" y="6121.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">独立性判断</text>
<text x="1866.0" y="6153.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">由标准化得到统计量分布</text>
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<rect x="2628.0" y="5966.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
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<text x="2653.0" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">89</text>
<text x="2680.0" y="6008.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W3 次序/极限</text>
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<text x="3342.1" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="2650.0" y="6057.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">次序统计量密度</text>
<text x="2650.0" y="6089.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">极差与 Uniform 特例</text>
<text x="2650.0" y="6121.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">CLT 近似</text>
<text x="2650.0" y="6153.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">两样本正态统计量</text>
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<rect x="3417.0" y="5972.5" width="760.0" height="220.0" rx="9" fill="#7DD3FC" opacity="0.22"/>
<rect x="3412.0" y="5966.5" width="760.0" height="220.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="3412.0" y="5966.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
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<circle cx="3437.0" cy="6001.5" r="16" fill="#E0F2FE" stroke="#0EA5E9" stroke-width="2.4"/>
<text x="3437.0" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">90</text>
<text x="3464.0" y="6008.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W4 充分性</text>
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<text x="4126.1" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="3434.0" y="6058.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">定义法： </text>
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1.393 73.098 1.393 Q 74.679 1.393 75.734 2.824 Q 76.792 4.258 76.792 6.409 Z M 85.902 1.458 L 81.880 1.458 Q 81.609 -0.434 81.886 -1.235 Q 82.234 -2.223 83.177 -2.223 Q 84.124 -2.223 84.846 -1.229 Q 85.477 -0.357 85.902 1.458 Z M 86.097 2.532 Q 86.268 4.329 86.046 4.960 Q 85.700 5.960 84.769 5.960 Q 83.802 5.960 83.094 4.972 Q 82.537 4.177 82.100 2.532 L 86.097 2.532 Z M 84.953 6.909 Q 86.471 6.909 87.078 5.567 Q 87.685 4.234 87.224 1.868 Q 86.768 -0.491 85.635 -1.830 Q 84.510 -3.178 82.993 -3.178 Q 81.469 -3.178 80.868 -1.830 Q 80.267 -0.491 80.722 1.868 Q 81.184 4.234 82.303 5.567 Q 83.430 6.909 84.953 6.909 Z M 94.172 14.040 Q 92.964 11.964 92.374 9.929 Q 91.787 7.897 91.787 5.810 Q 91.787 3.726 92.380 1.679 Q 92.972 -0.367 94.172 -2.437 L 92.727 -2.437 Q 91.374 -0.312 90.700 1.737 Q 90.027 3.787 90.027 5.810 Q 90.027 7.825 90.694 9.866 Q 91.365 11.909 92.727 14.040 L 94.172 14.040 Z M 96.747 13.491 L 108.156 13.491 L 107.867 11.953 L 103.052 11.953 L 100.739 0.003 L 98.906 0.003 L 101.219 11.953 L 96.449 11.953 L 96.747 13.491 Z M 108.438 14.040 L 109.883 14.040 Q 111.236 11.909 111.909 9.866 Q 112.583 7.825 112.583 5.810 Q 112.583 3.787 111.909 1.737 Q 111.236 -0.312 109.883 -2.437 L 108.438 -2.437 Q 109.637 -0.367 110.230 1.679 Q 110.823 3.726 110.823 5.810 Q 110.823 7.897 110.230 9.929 Q 109.637 11.964 108.438 14.040 Z M 124.480 6.111 L 123.295 0.003 L 121.624 0.003 L 122.810 6.047 Q 122.891 6.472 122.934 6.796 Q 122.980 7.122 122.980 7.310 Q 122.980 8.071 122.500 8.493 Q 122.023 8.918 121.165 8.918 Q 119.827 8.918 118.847 8.013 Q 117.867 7.111 117.578 5.614 L 116.485 0.003 L 114.823 0.003 L 117.560 14.060 L 119.222 14.060 L 118.147 8.530 Q 118.780 9.380 119.763 9.871 Q 120.749 10.363 121.833 10.363 Q 123.171 10.363 123.905 9.640 Q 124.642 8.918 124.642 7.608 Q 124.642 7.284 124.602 6.914 Q 124.561 6.544 124.480 6.111 Z M 131.633 14.040 Q 130.424 11.964 129.835 9.929 Q 129.248 7.897 129.248 5.810 Q 129.248 3.726 129.840 1.679 Q 130.433 -0.367 131.633 -2.437 L 130.187 -2.437 Q 128.834 -0.312 128.161 1.737 Q 127.487 3.787 127.487 5.810 Q 127.487 7.825 128.155 9.866 Q 128.826 11.909 130.187 14.040 L 131.633 14.040 Z M 144.218 10.120 L 139.573 5.160 L 142.420 0.003 L 140.512 0.003 L 138.373 4.015 L 134.650 0.003 L 132.635 0.003 L 137.613 5.333 L 134.968 10.120 L 136.873 10.120 L 138.815 6.461 L 142.203 10.120 L 144.218 10.120 Z M 145.546 14.040 L 146.992 14.040 Q 148.344 11.909 149.018 9.866 Q 149.691 7.825 149.691 5.810 Q 149.691 3.787 149.018 1.737 Q 148.344 -0.312 146.992 -2.437 L 145.546 -2.437 Q 146.746 -0.367 147.338 1.679 Q 147.931 3.726 147.931 5.810 Q 147.931 7.897 147.338 9.929 Q 146.746 11.964 145.546 14.040 Z" transform="translate(3434.05 6091.58) scale(1 -1)" fill="#111827"/>
<text x="3434.0" y="6125.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Poisson/几何/指数/正态模型</text>
<text x="3434.0" y="6157.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">支持含参注意 min/max</text>
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<rect x="4196.0" y="5966.5" width="760.0" height="216.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="4196.0" y="5966.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
<rect x="4196.0" y="5974.5" width="760.0" height="9" fill="#0EA5E9" opacity="0.20"/>
<circle cx="4221.0" cy="6001.5" r="16" fill="#E0F2FE" stroke="#0EA5E9" stroke-width="2.4"/>
<text x="4221.0" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">91</text>
<text x="4248.0" y="6008.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W5 矩估计</text>
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<text x="4910.1" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="4218.0" y="6057.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">二项两参、正态、Gamma、对数正态</text>
<text x="4218.0" y="6089.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">函数参数用代入</text>
<text x="4218.0" y="6121.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">无偏/渐近无偏判断</text>
<text x="4218.0" y="6153.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">矩估计不唯一</text>
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<rect x="4980.0" y="5966.5" width="760.0" height="218.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="4980.0" y="5966.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
<rect x="4980.0" y="5974.5" width="760.0" height="9" fill="#0EA5E9" opacity="0.20"/>
<circle cx="5005.0" cy="6001.5" r="16" fill="#E0F2FE" stroke="#0EA5E9" stroke-width="2.4"/>
<text x="5005.0" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">92</text>
<text x="5032.0" y="6008.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W6 MLE</text>
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<text x="5694.1" y="6007.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="5002.0" y="6058.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">可导模型： </text>
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<text x="5002.0" y="6091.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">支持含参：先找可行域</text>
<text x="5002.0" y="6123.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">非唯一 MLE 写集合</text>
<text x="5002.0" y="6155.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Uniform/双参数指数/0-1族</text>
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<rect x="1065.0" y="6218.5" width="760.0" height="216.0" rx="9" fill="#7DD3FC" opacity="0.22"/>
<rect x="1060.0" y="6212.5" width="760.0" height="216.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="1060.0" y="6212.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
<rect x="1060.0" y="6220.5" width="760.0" height="9" fill="#0EA5E9" opacity="0.20"/>
<circle cx="1085.0" cy="6247.5" r="16" fill="#E0F2FE" stroke="#0EA5E9" stroke-width="2.4"/>
<text x="1085.0" y="6253.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">93</text>
<text x="1112.0" y="6254.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W7 C-R</text>
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<text x="1774.1" y="6253.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="1082.0" y="6303.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">正则条件检查</text>
<text x="1082.0" y="6335.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">Fisher 信息量</text>
<text x="1082.0" y="6367.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">C-R 下界</text>
<text x="1082.0" y="6399.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">有效估计与估计量组合</text>
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<rect x="1849.0" y="6218.5" width="760.0" height="216.0" rx="9" fill="#7DD3FC" opacity="0.22"/>
<rect x="1844.0" y="6212.5" width="760.0" height="216.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="1844.0" y="6212.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
<rect x="1844.0" y="6220.5" width="760.0" height="9" fill="#0EA5E9" opacity="0.20"/>
<circle cx="1869.0" cy="6247.5" r="16" fill="#E0F2FE" stroke="#0EA5E9" stroke-width="2.4"/>
<text x="1869.0" y="6253.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">94</text>
<text x="1896.0" y="6254.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W8 区间估计</text>
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<text x="2558.1" y="6253.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="1866.0" y="6303.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">μ 的 Z/t 区间</text>
<text x="1866.0" y="6335.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">σ² 的 χ² 区间</text>
<text x="1866.0" y="6367.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">单侧限与样本量</text>
<text x="1866.0" y="6399.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">预测统计量</text>
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<rect x="2633.0" y="6218.5" width="760.0" height="216.0" rx="9" fill="#7DD3FC" opacity="0.22"/>
<rect x="2628.0" y="6212.5" width="760.0" height="216.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="2628.0" y="6212.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
<rect x="2628.0" y="6220.5" width="760.0" height="9" fill="#0EA5E9" opacity="0.20"/>
<circle cx="2653.0" cy="6247.5" r="16" fill="#E0F2FE" stroke="#0EA5E9" stroke-width="2.4"/>
<text x="2653.0" y="6253.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="15" font-weight="900" fill="#0369A1" text-anchor="middle">95</text>
<text x="2680.0" y="6254.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W9 两样本/非正态区间</text>
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<text x="3342.1" y="6253.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="13" font-weight="800" fill="#0369A1" text-anchor="middle">作业线</text>
<text x="2650.0" y="6303.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">两个正态均值差</text>
<text x="2650.0" y="6335.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">方差比 F 区间</text>
<text x="2650.0" y="6367.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">比例/Poisson/指数</text>
<text x="2650.0" y="6399.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">表格补全：条件-统计量-分布-区间</text>
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<rect x="3417.0" y="6218.5" width="760.0" height="216.0" rx="9" fill="#7DD3FC" opacity="0.22"/>
<rect x="3412.0" y="6212.5" width="760.0" height="216.0" rx="9" fill="#FFFFFF" stroke="#334155" stroke-width="2.2"/>
<rect x="3412.0" y="6212.5" width="760.0" height="9" rx="9" fill="#0EA5E9"/>
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<text x="3464.0" y="6254.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W10 单样本检验</text>
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<text x="4248.0" y="6254.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="22" font-weight="900" fill="#111827">W11 两样本检验</text>
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<text x="4218.0" y="6303.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">两均值差检验</text>
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<text x="5002.0" y="6335.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">MLE 不一定唯一</text>
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<text x="5002.0" y="6399.5" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="17" font-weight="650" fill="#334155">x̄ 与 S² 独立只在正态样本中成立</text>
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<text x="96" y="6537" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="16" font-weight="700" fill="#92400E">总路线：样本/统计量 → 抽样分布 → MOM/MLE → 枢轴区间 → H0 下统计量与拒绝域；本图只保留知识点与公式，不放原题和解题步骤。</text>
<text x="3400.0" y="6576" font-family="Microsoft YaHei, Noto Sans CJK SC, Source Han Sans SC, Arial, sans-serif" font-size="11" fill="#64748B" text-anchor="middle">数学公式为矢量路径，放大和打印清晰；中文说明仍为 SVG text。</text>
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