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Suppose that two teams play a series of games that ends when one of the teams has one i number of games. Suppose that each game played is,...

1. Suppose that two teams play a series of games that ends when one of the teams has one i number of 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 when (b) i = 3. Show also in both cases that this number is maximized when p = ½.
2. Consider problem 1 with i = 2. Find the variance of the number of games played and show that this number is maximized when p = ½.

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