方差转移定律

问题描述

精选答案

方差：

D(X) = (1) Σ(i=1->n) ni [xi-E(x)]^2

= (1) Σ(i=1->n) ni [xi^2+E^2(x)-2xiE(x)]

= (1) {Σ(i=1->n) nixi^2 + Σ(i=1->n) E^2(x) - 2E(x)Σ(i=1->n) xi}

= (1) Σ(i=1->n) nixi^2 + (1) Σ(i=1->n) E^2(x) - (1) 2E(x)Σ(i=1->n) xi

= 均方值 + 均值的平方 - 2倍均值的平方

= 均方值 - 均值的平方

= (1) Σ(i=1->n) (nixi^2) - E^2(x) (1)

E(X) = (1) Σ(i=1->n) ni xi (2)

n = Σ(i=1->n) ni (3)