Problem 1. Let X and Y be continuous random variables with joint probability density function given by Cr2 if x 0, x <4, x>-y, and r≥ y/2 f(x, y) 1,y) = { 0 otherwise. (a) The marginal density, fy (y), of Y. (Be explicit about all cases.) (b) The conditional density, fxy (2|2), of X given Y = 2. Be explicit about all cases! (c) P(X3 | Y= 2). (d) E(X | Y = 2). (e) P(X3 | Y≥ 2).