Exercise 8. Let X be a discrete random variable with probability mass function given by p(x) = 1/4 x = 0 1/2 x = 1 1/8 x = 2 1/8 x = 3

(a) Verify that p(x) is a valid probability mass function. (b) Find P (X 2). (c) Find P (X 2|X 1). (d) Find E(X).