Problem 1: You are given a coin and you are told that its bias (probability of heads) is either 131 or p2. Let 9 = 1 denote the case Where the bias of the coin is p1 and let G = 2 the case when the bias of the coin is 192. You are given that P( = 1) = q. Assume you ip it independently n times. Let X be the number of heads you get. Let Y = n X. (a) Find the mean X and Y. (3 points) (b) Find the variance of X and Y. (5 points)