A gambler initially having one chip participates in up to five rounds of gambling. In each round, the gambler bets all of her chips, and with probability on doubling the number of chips she has, and with probability one half, she loses all her chips Let X denote the number of chips the gambler has after five rounds, and let Y denote the maximum number of chips the gambler example, if the gambler wins in the first three rounds and loses in the fourth, Y 8. If the gambler loses in the first round, Y = 1 half, she wins, thereby e ever has (with stopping after five rounds). For (a) Find the pmf, mean, and variance of X (b) Find the pmf, mean, and variance of Y