5. (3pt total) (a) (1pt) Find all a > 0 for which there is a finite constant ca so that the function f(x) 1 Ca 1+ra is a probability density function. = Hint: You do not need to compute ca. For figuring out whether integrals are finite you might want to review the comparison test for improper integrals from calculus. (b) (1pt) Suppose that a > 0 is a number for which fa is a PDF. Suppose that X is a random variable with PDF fa. For which a > 0 will EX exist? (c) (1pt) Suppose that X has a PDF given by fa and X has a finite expectation. What is EX? Hint: You will not need to actually do any complicated integrations in this problem.