① To find E(X), first find the edge distribution density function fX(x) of X. According to the definition, FX (x) = ∫ (-∞, ∞) f (x, y) fy = ∫ (0, ∞) e (-x-y) dy = [e (-x)

(2) According to the expected definition. e(x)=∫(0,∞)xfx(x)dx=∫(0,∞)xe^(-x)dx= 1。

e(x+y)=∫(0,∞)∫(0,∞)(x+y)e^(-x-y)dxdy==∫(0,∞)∫(0,∞)xe^(-x-y)dxdy+∫(0,∞)∫(0,∞)ye^(-x-y)dxdy=2。

e[e^(-x)]=∫(0,∞)[e^(-x)]fx(x)dx=∫(0,∞)e^(-2x)dx= 1/2。

For reference.