设二维随机变量(X,Y)的概率密度为:f(x,y)=12y^2,0

问题描述:

设二维随机变量(X,Y)的概率密度为:f(x,y)=12y^2,0

EX=∫∫[01]∫[0->x] 12xy²dydx=4/5
EY=∫∫[01]∫[0->x] 12y³dydx=3/5
E(X²+Y²)=∫∫[01]∫[0->x] 12x²y²+12y^4dydx=16/15

EX=∫∫[0