设 X E(X)=μ,方差 D(X)=σ^2 令X'=(X-μ)/σ,求E(X') ,D(X')
问题描述：
设 X E(X)=μ,方差 D(X)=σ^2 令X'=(X-μ)/σ,求E(X') ,D(X')
答
E[（x-u)/sigma]=[E(x)-E(u)]/sigma=(u-u)/sigma=0
D[（x-u)/sigma]=D(x-u)/sigma^2=[D(x)+D(u)+2Cov(x,u)]/sigma^2
=1
D(u)=0,Cov(x,u)=Ex*E(u)-E(x)E(u)=0
答
E(X')=E[(X-μ)/σ]=[E(X)-u]/σ=0
D(X')=D[(X-μ)/σ]=[D(X)]/σ^2=1