Problem 3. Kafka and Milena play 900 rounds of rock-paper-scissors (all you need to know about rock- paper-scissors for this problem is that it is a two-player game in which ties are possible). Let us assume that neither player has any advantage, so that in each round, independently of all other rounds, the outcomes "Kafka wins", "Milena wins", and "tie" are equally likely. Let X be the number of rounds Kafka wins, and let Y be the number of rounds that were not ties. (a) (6 pts) Name the distributions of X and Y, and find the numerical values of their parameter(s). (b) (4 pts) Compute P(X = 500). Find E(X) and Var(X). (c) (4 pts) Compute P(Y = 200). Find E(Y) and Var(Y). (d) (6 pts) Compute E(Y2 - X2)