Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 80% of their games.To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob tenpoints the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points aslong as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage.It turns out that with a five-point advantage Bob wins 40% of the time; he wins 70% of the time with a ten-point advantage and90% of the time with a fifteen-point advantage.Model this situation as a Markov chain using the number of consecutive games won by Doug as the states. There should be fourstates representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrix of this system,the steady-state vector for system, and determine the proportion games that Doug will win the long run under theseconditions.0000000P = 00S = 00Proportion of games won by Doug = 0

There are two players, Bob and Doug. Doug is a much better player and wins 80% of their games. If…

Answered: Bob and Doug play a lot of Ping-Pong,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 26EQ

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Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games. To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage. It turns out that with a five-point advantage Bob wins 40% of the time; he wins 40% of the time with a ten-point advantage and 50% of the time with a fifteen-point advantage. Model this situation as a Markov chain using the number of consecutive games won by Doug as the states. There should be four states representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in…
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