Question 2 Sampling Distributions. (a) Let Y1, Y2, ..., Y, be a random sample of size n from some distribution (i.e. the Ya's are independent and identically distributed). Assuming all moment generating functions exist, find the MGF of the sample mean Y, my(t), in terms of the MGFs of the Y's, my (t). (b) Let Y1, Y2, ..., Y, a random sample of size n from a distribution with mean E(Y;) = / and variance V(Y ) = o'. Suppose the moment generating functions my (t) exist. Define Y - H Un = o/Vn Show that lim P(Un u) in terms of all of the Y's jointly. The result will be the complementary distribution function of another exponential distribution. There's no need to use MGFs here.)