Explanation Given: The stochastic matrix is [ .55 0 .45 1 ] . Approach: Consider the formula to compute the steady-state matrix for an absorbing stochastic matrix. An absorbing stochastic matrix A has been partitioned into submatrices. A = [ I 0 | S R ] …… (1) Then, the steady-state matrix A is given by A = [ I 0 | S ( I - R ) - 1 0 ] …… (2) Here, I is an identity matrix, 0 is the zero matrix and the order of the identity matrix appearing in the expression ( I − R ) − 1 is chosen to have the same order as R . Calculation: Since, The stochastic matrix is [ .55 0 .45 1 ] Rewrite the given matrix in the form of that the absorbing states appear first, partition the resulting matrix and identify the submatrices R and S . A = [ 1 0 | .45 .55 ] Compare the matrix element with equation (1). Here, the place of I is [ 1 ] , the place of zero matrix is [ 0 ] , the place of S is [ .45 ] and the place of R is [ .55 ] . Now, calculate the matrix S ( I − R ) − 1 .

Finite Mathematics for the Managerial, Life, and Social Sciences

12th Edition

ISBN: 9781337405782

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 9.3, Problem 15E

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To compute:

The steady-state matrix of the given stochastic matrix [.550.451].

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Chapter 9.3, Problem 14E

Chapter 9.3, Problem 16E

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Finite Mathematics for the Managerial, Life, and Social Sciences

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 of the given stochastic matrix [ .55 0 .45 1 ] .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

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To compute:

The steady-state matrix of the given stochastic matrix [.550.451].

Want to see the full answer?

Chapter 9 Solutions

The steady-state matrix of the given stochastic matrix [ .55 0 .45 1 ] .

Solution Summary: The author explains the formula to compute the steady-state matrix for an absorbing stochastic matrix.

Videos

To compute: The steady-state matrix of the given stochastic matrix [.550.451].

Want to see the full answer?

Chapter 9 Solutions

To compute:

The steady-state matrix of the given stochastic matrix [.550.451].