设二维随机变量(X,Y)的概率密度为:f(x,y)=12y^2,0
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设二维随机变量(X,Y)的概率密度为:f(x,y)=12y^2,0
设二维随机变量(X,Y)的概率密度为:f(x,y)=12y^2,0
设二维随机变量(X,Y)的概率密度为:f(x,y)=12y^2,0
EX=∫∫[0
EX=∫∫[0<=y<=x<=1] xf(x,y)dxdy=∫[0->1]∫[0->x] 12xy²dydx=4/5
EY=∫∫[0<=y<=x<=1] yf(x,y)dxdy=∫[0->1]∫[0->x] 12y³dydx=3/5
E(X²+Y²)=∫∫[0<=y<=x<=1] (x²+y²)f(x,y)dxdy=∫[0->1]∫[0->x] 12x²y²+12y^4dydx=16/15
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