设X1,X2.Xn(n>2)为来自总体N(0,a^2)的样本,记Yi=Xi-X的均值,

题目

设X1,X2.Xn(n>2)为来自总体N(0,a^2)的样本,记Yi=Xi-X的均值,
i=1,2...n.若C(Y1+Yn)^2是a^2的无偏估计求c

答案

X1,X2.Xn来自总体为N(0,σ^2)=>∑xi~N(0,nσ^2)=>∑xi/√(nσ^2)~N(0,1)=>[∑xi/√(nσ^2)]^2~x^2(1)=>C=nσ^2