2018 October 28,

Math 265: Day 20

Carleton College, Joshua R. Davis

A. Problem 8.9 #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.

B. What are the expectation and variance of T?

C. Now suppose that X and Y are both normal. Prove that T is also normal (with the expectation and variance that you computed in Problem B.)