Let (X, Y ) be a random vector described by a product pdf fXY (x, y) = fX(x)fY (y). Let FX and FY denote the corresponding marginal cdf's.
(a) Prove
(b) Assume, in addition, that X and Y are identically distributed, i.e., have the same pdf. Based on the result of (a) calculate the probability P(X>Y ).