4. Consider three rv's X, Y, and 2, which describe the electricity demand for March, June, and August, respectively. Because these are nonconsecutive months, assume that the rv's are independent. Let MX( t), M y( t), and Mz(t) be the moment generating functions for the three random variables, respectively. a) Let T be the total electricity demand for the months of March, June, and August combined. Write an expression for the mgf of T in terms of the mgf's of X, Y, and Z. Hint: Use the definition of joint mgf and the fact that the rv's here are independent. b) IfMX (t) : (1a 2t)'3,MY(t) : (17 2025, and M2 (r) : (17 2t) 45, find the mean and variance of T. Hint: There are several ways to do this problem, but it is probably easiest if you can identify the distribution of T first. c) Find E(X3)