HOMEWORK SOLUTIONS FOR MATH 5651 HOMEWORK FOR WEEK 5 OF SPRING 2011 Summary: HOMEWORK SOLUTIONS FOR MATH 5651 HOMEWORK FOR WEEK 5 OF SPRING 2011 Text: DeGroot and Schervish, 4th edition Note: Sometimes I write P instead of Pr because it is shorter. And I continue to use the notation AB = A B. Homework: §3.4: 2,3,4,5; §3.5: 2,4,6,8; (§3.6: 2,4,8,10 was also assigned for week 5, but the due date for this portion has been postponed to October 25, 2011. Accordingly, solutions for this portion of the homework will be posted later.) Problem 2 of §3.4 (a) P(X = 2) = 0.05 + 0.06 + 0.09 + 0.04 + 0.03 = 0.27. (b) P(Y 2) = 0.06 + 0.12 + 0.09 + 0.03 + 0.01 + 0.05 +0.04 + 0.03 + 0.01 + 0.02 + 0.03 + 0.04 = 0.53 (c) P(X 2 and Y 2) = 0.08 + 0.07 + 0.06 + 0.06 +0.10 + 0.12 + 0.05 + 0.06 + 0.09 = 0.69. (d) P(X = Y ) = 0.08 + 0.10 + 0.09 + 0.03 = 0.30. (e) P(X > Y ) = 0.06 + 0.06 + 0.03 + 0.05 + 0.03 + 0.02 = 0.25. Problem 3 of §3.4 We are given that discrete random variables X and Y have a discrete p.f. fX,Y (x, y) = c|x + y| for x, y = -2, -1, 0, 1, 2. Collections: Mathematics