 
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) = cx + y for x, y = 2, 1, 0, 1, 2.
