(a) Explanation Given: A security guard is equally likely to stay at the middle door or move to either the left door or the door to his right. If he is at the first door, he is equally likely to stay there or move to the door to his right, and if he is at the third door, he is equally likely to stay there or move to the door to his left. Explanation: Let the transition matrix for the provided information be denoted by P . 3 doors would correspond to a 3 × 3 transition matrix. Now, the first row of the transition matrix would represent the probabilities of the guard at door number 1, staying there, moving to door number 2, and moving to door number 3. Similarly, the second row would give the same probabilites if the guard was originally at the second or the middle door and the third row would give the probabilities for the guard’s movement when he is at door number 3. Let the probability for the guard to remian at the first door, the middle door, and the third door be represented by a , b , and c , respectively. Use the provided informtaion to set up the transition matrix as P . P = [ a a 0 b b b 0 c c ] The sum of the entries for a transition matrix should sum to 1 (b) To determine The fraction of time the guard spends at each door in the long run.

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.2, Problem 43E

(a)

To determine

To verify: The transition matrix for the provided information is [1212013131301212].

(b)

To determine

The fraction of time the guard spends at each door in the long run.

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Chapter 10.2, Problem 42E

Chapter 10.2, Problem 44E

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Chapter 10 Solutions

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

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To verify: The transition matrix for the provided information is [ 1 2 1 2 0 1 3 1 3 1 3 0 1 2 1 2 ] .

Solution Summary: The author explains how the transition matrix for the provided information is denoted by P.

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To verify: The transition matrix for the provided information is [1212013131301212].

The fraction of time the guard spends at each door in the long run.

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Chapter 10 Solutions