Mathematical expectation of continuous two-dimensional random variables
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。