Consider Problem 22 with i = 2. Find the variance of the number of games played, and show that this number is maximized when p = 1/2.
Problem 22
Suppose that two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when (a) i = 2 and (b) i = 3. Also, show in both cases that this number is maximized when p = 1/2.