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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.
Using a 1% level of significance, can we say that there is a difference in the average waiting time between the two shops? Find the critical value(s).
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Sketch the appropriate distribution, and locate the critical region for a = 0.05.
question past records show that the mean life of a certain brand of batteries used in a digital clock is 305 days.
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