Diana's son Isaac really likes being the Impostor in the game Among Us. Suppose games are independent and each time he has probability p of winning. (a) Suppose Isaac plays until he wins k times. It takes him Y (a r.v.) games to get these wins, and then he will play an additional Y games, and then stop. Find the mean total number of wins. (b) Find the variance of the total number of wins in (a). (c) Now suppose Isaac plays n games. He wins X (a r.v.) of these games, and then he will play an additional X games, and then stop. Find the mean total number of wins. (d) Find the variance of the total number of wins in (c). (Hint: you will need to consider the covariance of the number of wins on the first n games (X) and the number of wins on the additional X games, since they are not independent.) (e) Find the probability he wins 0 of the additional games in the situation in (c).