设随机变量X与Y相互独立,且D(X)=3,D(Y)=4,求D(X-4Y)
问题描述:
设随机变量X与Y相互独立,且D(X)=3,D(Y)=4,求D(X-4Y)
答
D(X-4Y)=D(X)-2Cov(X,4Y)+D(4Y)=D(X)+D(4Y)=D(X)+16D(Y)=3+16*4=67
设随机变量X与Y相互独立,且D(X)=3,D(Y)=4,求D(X-4Y)
D(X-4Y)=D(X)-2Cov(X,4Y)+D(4Y)=D(X)+D(4Y)=D(X)+16D(Y)=3+16*4=67