Problem 4 (30 points) There are two "independent" games: . In the first game, the possible rewards are fo, 1,2) and probabilities of getting the rewards are: . In the second game, the possible rewards are (10,20,30) and probabilities of getting the rewards are: P(10) = 1, P(20)-j. P(30)-|. Define X to be the multiplication of the rewards obtained from game I and game 2. Part a Calculate PMF of X, EX] and Var[X]. Part b Calculate E 2X+4 and Var 3.X+ 6)