A certain drugstore has three public telephone booths. For i = 0, 1, 2, 3, let pi denote the probability that exactly i telephone booths will be occupied on any Monday evening at 8:00 p.m.; and suppose that p0 = 0.1, p1 = 0.2, p2 = 0.4, and p3 = 0.3. Let X and Y denote the number of booths that will be occupied at 8:00 p.m. on two independent Monday evenings. Determine:
(a) The joint p.f. of X and Y;
(b) Pr(X = Y);
(c) Pr(X > Y).