2019 November 1,

Math 265: Day 20

Carleton College, Joshua R. Davis

A. Section 8.9 Exercise 1.

B. Section 8.9 Exercise 3.

C. Section 8.9 Exercise 11.

D. Problem 8.9 Exercise 22 (Laplace distribution).

For these next two problems, suppose that X and Y are two independent random variables, which both have expectation μ and variance σ². Let T = X + Y.

E. What are the expectation and variance of T?

F. Now suppose that X and Y are both normal. Prove that T is also normal using convolution. (You know the parameters of that normal distribution from the previous problem.)