Explanation Approach: If T is a regular stochastic matrix, then 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: Consider the matrix, [ 0.6 0.4 0.3 0.3 0.3 0.3 0.1 0.3 0.4 ] Let, X = [ x y z ] Be a steady state vector associated with the Markov process, where x and y are to be determined. The condition T X = X translates into the matrix equation, [ 0.6 0.4 0.3 0.3 0.3 0.3 0.1 0.3 0.4 ] [ x y z ] = [ x y z ] Solve the above matrix equation, [ 0.6 x + 0.4 y + 0.3 z 0.3 x + 0.3 y + 0.3 z 0.1 x + 0.3 y + 0.4 z ] = [ x y z ] Equivalently, the linear system of equation for above matrix equation is, 0.6 x + 0.4 y + 0.3 z = x 0.3 x + 0.3 y + 0.3 z = y 0.1 x + 0

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 3TE

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The steady state for matrix in example 4 is X=[0.470.300.23].

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Chapter 9.2, Problem 2TE

Chapter 9.3, Problem 1CQ

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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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To Verify: The steady state for matrix in example 4 is X = [ 0.47 0.30 0.23 ] .

Solution Summary: The author proves that the steady state vector of the matrix in example 4 is X=left[c0.47 0.30

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To Verify:

The steady state for matrix in example 4 is X=[0.470.300.23].

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Chapter 9 Solutions

To Verify: The steady state for matrix in example 4 is X = [ 0.47 0.30 0.23 ] .

Solution Summary: The author proves that the steady state vector of the matrix in example 4 is X=left[c0.47 0.30

Videos

To Verify: The steady state for matrix in example 4 is X=[0.470.300.23].

Want to see the full answer?

Chapter 9 Solutions

To Verify:

The steady state for matrix in example 4 is X=[0.470.300.23].