设样本X1,X2,...,X5来自总体N(0,1),Y=c(x1+x2)⼀(x3^+x4^+x5^

2024-11-22 23:11:39
推荐回答(2个)
回答1:

因为样本X1,X2...X5,来自总体N(0,1),所以X1+X2~N(0,2)
A=(X1+X2)/2^0.5~N(0,1),即X1+X2=A*2^0.5;
B=(X3^2+X4^2+X5^2)~X^2(3),即X3^2+X4^2+X5^2=B;
由t分布的定义Y=A/(B/3)^0.5~t(3)
即Y=C*(A*2^0.5)/(B)^0.5=A/(B/3)^0.5;
故2^0.5*C=3^0.5,即C=(1.5)^0.5

回答2: