Explanation Approach: Take the initial distribution to be X , the steady-state distribution vector. Then, when n is large, X ≈ T n X . Multiply both sides of the last equation by T and consider the resultant equation when n is large. Calculation: Let’s take the initial distribution to be X , the steady-state distribution vector. The X contains x 1 , x 2 , ... x n . The vector equation be, T X = X … (1) Then, when n is large, according to the definition of steady state distribution vectors, X ≈

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

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Chapter 9.2, Problem 29E

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The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Chapter 9.2, Problem 28E

Chapter 9.2, Problem 1TE

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Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

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 steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

Solution Summary: The author explains that the steady-state distribution vector X can be found by solving the vector equation TX=X with the condition that sum of the elements of is 1.

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To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

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Chapter 9 Solutions

The steady-state distribution vector X may be found by solving the vector equation T X = X together with the condition that the sum of the elements of X is 1.

Solution Summary: The author explains that the steady-state distribution vector X can be found by solving the vector equation TX=X with the condition that sum of the elements of is 1.

Concept explainers

Videos

To show: The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.

Want to see the full answer?

Chapter 9 Solutions

To show:

The steady-state distribution vector X may be found by solving the vector equation TX=X together with the condition that the sum of the elements of X is 1.