Answered: Alan and Betty play a series of games…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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Question

Alan and Betty play a series of games with Alan winning each game independently with probability p = 0.6. The overall winner is the first player to win two games in a row.

Define a Markov chain to model the above problem.

Expert Solution

Step 1

Given information:

P(Win) = 0.60

P(Loss) = 1 - P(Win)

P(Loss) = 1 - 0.60

P(Loss) = 0.40

Three state Markov model can be defined for the given scenario:

State 1: Zero wins

State 2: Wins (When previous round was lost)

State 3: Wins (When previous round was Won)

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