设(X,Y)的概率密度为f(x,y)={e-y,0≤x≤1,y>0{0,其他.求E(X+Y).

设(X,Y)的概率密度为
f(x,y)=
{e-y,0≤x≤1,y>0
{0,其他.
求E(X+Y).
【正确答案】:E(X+Y)=∫+∞-∞+∞-∞(x+y)f(x,y)dxdy=∫10(∫+∞0(x+y)(e-ydy)dx=∫10(x+1)dx=3/2