Consider Problem 4.22 with i = 2. Find the variance of the number of games played, and show that this number is maximized when p = 1/2.

Problem 4.22

Suppose that two teams play a series of games that ends when one of them has won games. Suppose that each game played is, independently, won by team with probability . 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.