Problem 1. (30 points.) Let X and Y be random variables such that X~ Exponential(1); and the conditional distribution of Y given that X = x is Uniform (0, 1/x). (a) Determine f(x, y). the joint p.d.f. of X and Y. Specify the domain where f(x, y) > 0. (b) Determine fy (y). the marginal p.d.f. of Y. Specify the domain where fy (y) > 0. (c) Determine f(xly = 1). the conditional p.d.f. of X given that Y = 1.