2018 November 6,

Math 265: Day 23

Carleton College, Joshua R. Davis

A. Section 9.9 Exercise 6

B. Section 9.9 Exercise 14

C. Section 9.9 Exercise 22a. (Part b is no longer required. If you want to do it, try using Theorem 9.5.4, which we haven't studied. I made this change on the morning of Tuesday November 6.)

D. Section 9.9 Exercise 31a

E. Let X and Y be jointly distributed continuous random variables with f_X,Y(x, y) = e^{-(x + 1)y} for 0 < x < e - 1 and y > 0. First, find E(Y | X = x) and E(Y | X). Second, find E(Y) in two ways: via the law of total expectation, and via the usual way (using the distribution of Y). (There was a typographical error in the original version of this problem. I fixed it on the evening of Saturday November 3.)