1 MGFs n=0 Given a random variable X, the moment generating function of X is defined as the function My(t)= E[e/X]. Moment generating functions, or MGFs for short, are immensely useful because of the Taylor expansion X = 1 +fX+ (1x)2 (1x) ( 2! 3! n! By taking the kth derivative of the MGF of X with respect to t and evaluating at t=0, we can gen- erate the kth moment of X, (i.e. the value of E [Xk]) without having to do any painful integration! (a) Compute the moment generating function Mx (t) of X, where X ~ Expo(2), for t