2. (20 points) You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let N be the number of times the two dice have to be rolled before the game is decided. (a) (3 points) What is the probability mass function (pmf) of N? (b) (2 points) Compute E(N). (c) (5 points) What is the probability that you win the game? (d) (10 points) Assume that you will gain $10 for winning in the first round, $1 for winning in any other round, and nothing otherwise. Compute your expected winnings in the game.