1. [Joint PMF] An IC manufacturing company is testing six IC chips they have created, two of which are defective. To determine which chips are defective, they test each of them individually one at a time. Let M, be the number of chips tested until the first defective is identified. Let My be the number of additional chips tested until the second defective chip is detected. (a) Find the joint pmf, PM,,M2 (1, j), for all i and j. (b) Find the marginal pmf PM. (2). (c) Find the marginal pmf PM2 (j). (d) Are M, and M2 independent? Justify your answer. (e) Find P(M2 > M1). (f) Find P(M2 = M1). (g) Find P(M1 = 4/M2 = 1)