容量分别是n1,n2.组成一个联合样本n1+n2,组合样本的方差是? n1与n2是相互独立的高斯随机变量,均值为0,方差为σ2,x...

\u8bbe\u603b\u4f53X\uff5eN\uff08\u03bc1\uff0c\u03c32\uff09\uff0c\u603b\u4f53Y\uff5eN\uff08\u03bc2\uff0c\u03c32\uff09\uff0c\u4e14\u4e24\u4e2a\u603b\u4f53\u76f8\u4e92\u72ec\u7acb\uff0e\u4ece\u603b\u4f53X\u548cY\u4e2d\u5206\u522b\u53d6\u5bb9\u91cf\u4e3an1\uff0cn2\u7684

\u7531\u5361\u65b9\u5206\u5e03\u7684\u6027\u8d28\u6709\uff1a(n1?1)S21\u03c32\uff5eX2\uff08n1-1\uff09\uff0c(n2?1)S22\u03c32\uff5eX2\uff08n2-1\uff09\u6545\uff1aD\uff08(n1?1)S21\u03c32\uff09=2\uff08n1-1\uff09(n1?1)2\u03c34DS21=2\uff08n1-1\uff09DS21=2\u03c34n1?1\u540c\u7406\u53ef\u5f97\uff1aDS22=2\u03c34n2?1\u6240\u4ee5\u6709\uff1aD\uff08S12+S22\uff09=2\u03c34n1?1+2\u03c34n2?1=2(n1+n2?2)(n1?1)(n2?1)\u03c34\uff0e

\u9898\u76ee\u4e0d\u660e\u3002

组合样本的方差是 S1^2 + S2^2

This problem is not as simple as the answer suggests here. When combining m random variables: n1, n2, ..., nm each with an average value of X1, X2, ..., Xm and a standard deviation S1, S2, ..., Sm, the average of the new random variable N = n1 + n2 + ... + nm will have an average value of X = X1 + X2 + ... + Xm, this is expected. The standard deviation of the new random variable, though, is S = (S1^2 + S2^2 + ... + Sm^2)^(1/2). So the variance of the new random variable or Var(N) = S1^2 + S2^2 + ... + Sm^2

配对样本还是独立样本?

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