设总体X~N(0,1),X1,X2,X3是来自X的样本,x为样本均值,则X3-x~___分布

问题描述:

设总体X~N(0,1),X1,X2,X3是来自X的样本,x为样本均值,则X3-x~___分布

x=1/3(X1+X2+X3)X3-x=X3-1/3(X1+X2+X3)=-1/3X1-1/3X2+2/3X3所以E(X3-x)=-1/3EX1-1/3EX2+2/3EX3=0Var(X3-x)=1/9Var(X1)+1/9Var(X2)+4/9Var(X3)=1/9+1/9+4/9=2/3所以X3-x~N(0,2/3)