1. [10 points total, 4+6] A random variable has a Pareto distribution with parameters a > 0 and xo > 0 if its density function is f(x)= Ta+1 0 for > To otherwise. (a) Show that f(x) is a probability density function. (b) Find E(X) and Var(X). 2. [6 points total, 3 points each] Suppose X and Y are random variables with joint probability density function f(x) = Sce-(0.5x+0.2y) for x 0 and y 0 0 (a) Find c such that f(x, y) is a joint PDF. otherwise. (b) Find the probabilities of P(X 2, Y