Two dice are tossed. Let X be the smaller number of points. Let Y be the larger number of points. If both dice show the same number, say, z points, then X = Y = z.
(a) Find the joint probability mass function of (X, Y).
(b) Are X and Y independent? Explain.
(c) Find the probability mass function of X. (d) If X = 2, what is the probability that Y = 5?