Explanation Given: The given matrix is, [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] Approach: When the power T m of the transition matrix T tends toward a fixed matrix as m get larger and larger. In this case, the limiting matrix is the steady-state matrix for the transition matrix. Calculation: Consider the given matrix. T = [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] Calculate T 2 as follows, T 2 = [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] = [ 0.5 0.44 0.41 0.2 0.2 0.2 0.3 0.36 0.39 ] Calculate T 3 as follows, T 3 = [ 0.5 0.44 0.41 0.2 0.2 0.2 0.3 0.36 0.39 ] [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] = [ 0.47 0.452 0.443 0.2 0.2 0.2 0.33 0.348 0.357 ] Calculate T 4 as follows, T 4 = [ 0.47 0.452 0.443 0.2 0.2 0.2 0.33 0.348 0.357 ] [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] = [ 0.461 0.4556 0.4529 0.2 0.2 0.2 0.339 0.3444 0.3471 ] Calculate T 5 as follows, T 5 = [ 0.461 0.4556 0.4529 0.2 0.2 0.2 0.339 0.3444 0.3471 ] [ 0.6 0.4 0.3 0.2 0.2 0.2 0.2 0.4 0.5 ] = [ 0.3417 0.3433 0.4559 0.2 0.2 0.2 0.3417 0.3433 0.3441 ] Calculate T 6 as follows, T 6 = [ 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.CRE, Problem 13CRE

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The steady-state matrix for the transition matrix.

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Chapter 9.CRE, Problem 12CRE

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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 matrix for the transition matrix.

Solution Summary: The author explains the steady-state matrix for the transition matrix. When the power Tm of the matrix T tends toward a fixed matrix as m get larger and larger, the limiting matrix is

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To find: The steady-state matrix for the transition matrix.

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To find:

The steady-state matrix for the transition matrix.