Question

一道概率论的题目,急救啊抽取样本（x1,x2,x3,x4),N(0,3^2),Y=(x1-x2)^2+(x3+x4)^2

Answer 1

X1-X2,X3+X4~N(0,2*3^2)

当c=1/18时,且仅在此时,√c(X1-X2),√c(X3+X4)~N(0,1),

cY=c[(x1-x2)^2+(x3+x4)^2]

=[√c(X1-X2)]^2+[√c(X3+X4)]^2~X(2)^2.