2. Suppose that two teams play a series of games that ends when one of them has won 2 games. Suppose that each game played is, independently, won by team A with probability p. Let X be the number of games played. (a) Find the pmf for X. All probabilities should be in terms of p. (b) Find the expected number of games that are played. E[X] will be in terms of p. (c) Show that this number is maximized when p = 1/2. Hint: consider local extrema of g(p) = E[X].

2. Suppose that two teams play a series of games that ends when one of them has won 2 games. Suppose that each game played is, independently, won by team A with probability p. Let X be the number of games played. (a) Find the pmf for X. All probabilities should be in terms of p. (b) Find the expected number of games that are played. E[X] will be in terms of p. (c) Show that this number is maximized when p = 1/2. Hint: consider local extrema of g(p) = E[X].

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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