Tutorial 7 1. Consider an ordinary deck of 52 cards comprised of the four "suits" spades, hearts, diamonds, and clubs, with each suit consisting of the 13 denominations ace, king, queen, jack, ten, ..., and two. Suppose now that only two cards are randomly selected from the deck. Let X be the number of diamond cards in the two-card hand. The pmf of X is given by: x 0 1 2 P(X = x) 0.559 0.382 0.059 a) Calculate the expected value of X. b) Calculate the variance of X. c) Determine the mgf of X.