Alice and Bob are playing a game where in each round, each of them rolls a fair die indepen-dently. If both roll the same number, then the game is repeated. Otherwise the player withthe larger number wins. LetXbe the number of rounds until the game is decided.(a) (10 points) Determine the probability mass function ofX.(b) (5 points ) ComputeE[X].(c) (5 points ) Compute Pr[ Alice win].(d) (5 points) Assume that you get paid 10USD for winning in the first round, 1USD forwinning in any other round, and nothing otherwise. Compute your expected winnings.