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You have two opponents with whom you alternate play. Whenever you play A, you win with probability PA; whenever you play B, you win with probability PB, where PB > PA. If your objective is to minimize the expected number of games you need to play to win two in a row, should you start with A or with B? Hint: Let E[N] denote the mean number of games needed if you initially play i. Derive an expression for E[NA] that involves E[N]; write down the equivalent expression for E[NB] and then subtract.

You have two opponents with whom you alternate play. Whenever you play A, you win with probability PA; whenever you play B, you win with probability PB, where PB > PA. If your objective is to minimize the expected number of games you need to play to win two in a row, should you start with A or with B? Hint: Let E[N] denote the mean number of games needed if you initially play i. Derive an expression for E[NA] that involves E[N]; write down the equivalent expression for E[NB] and then subtract.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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alternate play. You have two opponents with whom you Whenever you play A, you win with probability PA; whenever you play B, you win with probability PB, where PB > PA. If your objective is to minimize the expected number of games you need to play to win two in a row, should you start with A or with B? Hint: Let E[N] denote the mean number of games needed if you initially play i. Derive an expression for E[NA] that involves E[NB]; write down the equivalent expression for E[NB] and then subtract.
Transcribed Image Text:alternate play. You have two opponents with whom you Whenever you play A, you win with probability PA; whenever you play B, you win with probability PB, where PB > PA. If your objective is to minimize the expected number of games you need to play to win two in a row, should you start with A or with B? Hint: Let E[N] denote the mean number of games needed if you initially play i. Derive an expression for E[NA] that involves E[NB]; write down the equivalent expression for E[NB] and then subtract.
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