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Unformatted text preview: e, if n = 24 and p = 1/3, the pmf is maximized at
k ∗ = 8, as seen in Figure 2.5.
A number m is called a median of the binomial distribution if k:k≤m p(k ) ≥ 0.5 and k:k≥m p(k ) ≥
0.5. It can be shown that any median m of the binomial distribution satisﬁes
m − np ≤ max{p, 1 − p}.1 , so the median is always close to the mean, np.
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R. Kaas and J.M. Buhrman, ”Mean, median, and mode in binomial distributions,” Statistica Neerlandica, vol
34, no. 1, pp. 13  18, 2008. 36 CHAPTER 2. DISCRETETYPE RANDOM VARIABLES Example 2.4.9 Suppose two teams, A and B , play a bestofseven series of games. Assume that
ties are not possible in each game, that each team wins a given game with probability one half, and
the games are independent. The series ends once one of the teams has won four games, because
after winning four games, even if all seven games were played, that team would have more wins
than the other team, and hence it wins the series. Let Y denote the total number of games played.
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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