D(x)=9,D(y)=4,xy相关系数为0.4,求D（x+2y)

题目

D(x)=9,D(y)=4,xy相关系数为0.4,求D（x+2y)
急用

答案

D（x+2y)=D(x)+4D(y)+2E{(x-E(x))(2y-E(2y))}
=D(x)+4D(y)+4E{(x-E(x))(y-E(y))}
=D(x)+4D(y)+4Cov(x,y)
=D(x)+4D(y)+4ρxy*根号下（D(x)D(y)）
=9+16+4*0.4*3*2
=34.6