a. Explanation Consider that the walker starts at state 4. Observe that the graph is directed. Hence, obtain the transition matrix for a directed walk on the given graph. P = [ 0 1 2 0 0 0 0 0 1 2 0 0 1 1 2 0 1 2 1 0 0 1 2 0 0 0 0 0 1 2 0 ] Thus, obtain the transition matrix in canonical form with the states in the order 2, 1, 3, 4, 5 as follows. Rearrange the columns such that the column 2 is shifted the first column and hence the order of remaining column are changed accordingly. 2 1 3 4 5 [ 0 1 2 0 0 0 0 0 1 2 0 0 1 1 2 0 1 2 1 0 0 1 2 0 0 0 0 0 1 2 0 ] → column arrange [ 1 2 0 0 0 0 0 0 1 2 0 0 1 2 1 0 1 2 1 0 0 1 2 0 0 0 0 0 1 2 0 ] Similarly, row 2 is moved to row 1 as, [ 1 2 0 0 0 0 0 0 1 2 0 0 1 2 1 0 1 2 1 0 0 1 2 0 0 0 0 0 1 2 0 ] → row arrange [ 0 0 1 2 0 0 1 2 0 0 0 0 1 2 1 0 1 2 1 0 0 1 2 0 0 0 0 0 1 2 0 ] Change state 1 as the absorbed state b. To determine To find: The expected number of steps before the walker reaches state 2.

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

5th Edition

ISBN: 9781323132098

Author: Thomas, Lay

Publisher: PEARSON C

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Chapter 10.5, Problem 16E

To determine

To find: The expected number of visits by the walker when begins at state 4 to state 3 before the walker visits state 2.

To determine

To find: The expected number of steps before the walker reaches state 2.

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Chapter 10.5, Problem 15E

Chapter 10.5, Problem 17E

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Chapter 10 Solutions

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

Ch. 10.1 - Fill in the missing entries in the stochastic...Ch. 10.1 - Prob. 2PP Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - In Exercises 5 and 6, the transition matrix P for...Ch. 10.1 - Prob. 6E Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...

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The expected number of visits by the walker when begins at state 4 to state 3 before the walker visits state 2.

Solution Summary: The author explains how to obtain the transition matrix in canonical form with the states in the order 2, 1, 3, 4, 5 as follows.

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To find: The expected number of visits by the walker when begins at state 4 to state 3 before the walker visits state 2.

To find: The expected number of steps before the walker reaches state 2.

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Chapter 10 Solutions