Explanation Given: The given matrix is, [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] 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 = [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] Calculate T 2 as follows, T 2 = [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] = [ 0.43 0.34 0.22 0.27 0.3 0.3 0.3 0.36 0.48 ] Calculate T 3 as follows, T 3 = [ 0.43 0.34 0.22 0.27 0.3 0.3 0.3 0.36 0.48 ] [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] = [ 0.277 0.31 0.37 0.297 0.294 0.282 0.426 0.396 0.348 ] Calculate T 4 as follows, T 4 = [ 0.277 0.31 0.37 0.297 0.294 0.282 0.426 0.396 0.348 ] [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] = [ 0.3427 0.3274 0.3022 0.2871 0.2898 0.2934 0.3702 0.3828 0.4044 ] Calculate T 5 as follows, T 5 = [ 0.3427 0.3274 0.3022 0.2871 0.2898 0.2934 0.3702 0.3828 0.4044 ] [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] = [ 0.3138 0.3204 0.3315 0.2917 0.2907 0.2889 0.3945 0.3889 0.3796 ] Calculate T 6 as follows, T 6 = [ 0.3138 0.3204 0.3315 0.2917 0.2907 0.2889 0.3945 0.3889 0.3796 ] [ 0.1 0.2 0.6 0.3 0.4 0.2 0.6 0.4 0.2 ] = [ 0.3264 0.3235 0.3187 0.2897 0.2902 0.2909 0.3839 0.3863 0.3904 ] Calculate T 7 as follows, T 7 = [ 0.3264 0

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

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ISBN: 9781305283831

Author: Tan

Publisher: Cengage Learning

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Chapter 9.CRE, Problem 14CRE

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The steady-state matrix for the transition matrix.

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Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom 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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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.