Explanation Given Information: The provided regular stochastic matrix is, [ 1 0 0 1 8 1 4 0 1 0 1 8 0 0 0 1 0 1 4 0 0 0 1 4 1 2 0 0 0 1 2 0 ] Formula used: If an absorbing stochastic matrix is in the form of [ I S 0 R ] then its stable matrix is [ I S ( 1 − R ) − 1 0 0 ] . If a matrix is in the form of A = [ a b c d ] then its inverse is, A − 1 = [ d D − b D − c D a D ] Where, the value of D is, D = a d − b c ≠ 0 Calculation: Consider an absorbing stochastic matrix, [ 1 0 0 1 8 1 4 0 1 0 1 8 0 0 0 1 0 1 4 0 0 0 1 4 1 2 0 0 0 1 2 0 ] Rearrange the stochastic absorbing matrix in the form of [ I S 0 R ] . [ 1 0 0 1 8 1 4 0 1 0 1 8 0 0 0 1 0 1 4 0 0 0 1 4 1 2 0 0 0 1 2 0 ] = [ I S 0 R ] Identify the matrix S and R . The matrix S is, S = [ 1 8 1 4 1 8 0 0 1 4 ] The matrix R is, R = [ 1 4 1 2 1 2 0 ] Calculate the value of ( I − R ) . I − R = [ 1 0 0 1 ] − [ 1 4 1 2 1 2 0 ] = [ 1 − 1 4 0 − 1 2 0 − 1 2 1 − 0 ] = [ 3 4 − 1 2 − 1 2 1 ] = [ a b c d ] Substitute a = 3 4 , b = − 1 2 , c = − 1 2 and d = 1 in D = a d − b c

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ISBN: 9781323788707

Author: Goldstein

Publisher: PEARSON

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Chapter 8, Problem 8RE

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To calculate: The stable matrix of an absorbing stochastic matrix,

[10018140101800010140001412000120]

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Chapter 8, Problem 7RE

Chapter 8, Problem 9RE

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Chapter 8 Solutions

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The stable matrix of an absorbing stochastic matrix, [ 1 0 0 1 8 1 4 0 1 0 1 8 0 0 0 1 0 1 4 0 0 0 1 4 1 2 0 0 0 1 2 0 ]

Solution Summary: The author explains how to calculate the stable distribution of an absorbing stochastic matrix.

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To calculate: The stable matrix of an absorbing stochastic matrix,

[10018140101800010140001412000120]

Want to see the full answer?

Chapter 8 Solutions

The stable matrix of an absorbing stochastic matrix, [ 1 0 0 1 8 1 4 0 1 0 1 8 0 0 0 1 0 1 4 0 0 0 1 4 1 2 0 0 0 1 2 0 ]

Solution Summary: The author explains how to calculate the stable distribution of an absorbing stochastic matrix.

Videos

To calculate: The stable matrix of an absorbing stochastic matrix, [10018140101800010140001412000120]

Want to see the full answer?

Chapter 8 Solutions

To calculate: The stable matrix of an absorbing stochastic matrix,

[10018140101800010140001412000120]