Question 3 Distributions related to the exponential distribution. (a) Let Y be from a "shifted exponential distribution" which has density fy(y) = le (#" for y > a. Find the Moment Generating Function my(t). (Hint: See Midterm 1 Question 3(d). Write Y in terms of a "non-shifted" exponential random variable, as in the solutions to Midterm 1, and find the MGF of that.) (b) Let Y be a "standardized gamma" random variable. That is, let X ~Gamma(a, B) and define Y = X-QB VaBZ (noting that E(X) = of and Var(X) = of2). Use the moment generating function of Y to show that the limiting distribution of Y is Normal as o -> co. (Hint: Get the limit to look like the following, and then use the following fact: lim e (1- = 0-+00 etz/2)