Explanation Given: If the mouse turned left in the previous trial then the probability that mouse will turn left in the next trial is 0.8, and the probability that it will turn right is 0.2. If the mouse turned right in the previous trial, then the probability that it will turn right in the next trial is 0.1 whereas the probability that it will turn left is 0.9. Approach: Use the given data to make a transition matrix and then find the steady state vector of the transition matrix. The Steady state distribution vector X can be found by solving the vector equation, T X = X Together with the condition that the sum of the elements of the vector X should be equal to 1. Calculation: The transition matrix associated with the Markov chain is given by, T = [ 0.8 0.9 0.2 0.1 ] Let, X = [ x y ] Be a steady state vector associated with the Markov process, where x and y are to be determined. The x represents the percentage of the time will the mouse turn left at the T-junction and y represents the percentage of the time will the mouse turn right at the T-junction The condition T X = X translates into the matrix equation, [ 0.8 0.9 0.2 0.1 ] [ x y ] = [ x y ] Solve the above matrix equation, [ 0.8 x + 0.9 y 0.2 x + 0.1 y ] = [ x y ] Equivalently, the linear system of equation for above matrix equation is,

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ISBN: 9780100478183

Author: Tan

Publisher: YUZU

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Chapter 9.2, Problem 17E

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The percentage of the time will the mouse turn left at the T-junction in the long run.

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Chapter 9.2, Problem 16E

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Chapter 9 Solutions

EBK FINITE MATHEMATICS FOR THE MANAGERI

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

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The percentage of the time will the mouse turn left at the T-junction in the long run.

Solution Summary: The author explains how the probability of mouse turning left at the T-junction in the long run is 81.8%.

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The percentage of the time will the mouse turn left at the T-junction in the long run.

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