4.22. Suppose that two teams play a series of games that ends when one of them has won i 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 (b) i = 3. Also, 1 show in both cases that this number is maximized when p = 2 llo for 32 A 30 You hav $1000 cortain commodity

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
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4.22. How can I find the expected number of games that...? How could I show that ?

4.22. Suppose that two teams play a series of games that ends when
one of them has won i 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 (b) i = 3. Also,
show in both cases that this number is maximized when p
1
2
Voi hovo $1000 and a certain commodity procently collo for
Transcribed Image Text:4.22. Suppose that two teams play a series of games that ends when one of them has won i 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 (b) i = 3. Also, show in both cases that this number is maximized when p 1 2 Voi hovo $1000 and a certain commodity procently collo for
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