Solved: In Exercise 5.3, we determined that the joint probability distribution of Y1

Chapter 5, Problem 5.22

(choose chapter or problem)

In Exercise 5.3, we determined that the joint probability distribution of Y1, the number of married executives, and Y2, the number of never-married executives, is given by p(y1, y2) = 4 y1 3 y2 2 3 y1 y2 9 3 where y1 and y2 are integers, 0 y1 3, 0 y2 3, and 1 y1 + y2 3. a Find the marginal probability distribution of Y1, the number of married executives among the three selected for promotion. b Find P(Y1 = 1|Y2 = 2). c If we let Y3 denote the number of divorced executives among the three selected for promotion, then Y3 = 3 Y1 Y2. Find P(Y3 = 1|Y2 = 1). d Compare the marginal distribution derived in (a) with the hypergeometric distributions with N = 9, n = 3, and r = 4 encountered in Section 3.7. 5.22 I y1 y2 0 1 Total 0 .38 .17 .55 1 .14 .02 .16 2 .24 .05 .29 Total .76 .24 1.00 a Give the marginal probability functions for Y1 and Y2. b Give the conditional probability function for Y2 given Y1 = 0. c What is the probability that a child survived given that he or she was in a car-seat belt?