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 1 8 1 1 5 8 0 0 1 4 0 ] 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 1 8 1 1 5 8 0 0 1 4 0 ] [ x y z ] = [ x y z ] Solve the above matrix equation, [ 1 8 y + z x + 5 8 y 1 4 y ] = [ x y z ] Equivalently, the linear system of equation for above matrix equation is, 1 8 y + z = x x + 5 8 y = y 1 4 y = z The condition is that sum of x y , and z is 1. So, now we have four equations as, x + y + z = 1 ⋯ ( 1 ) 1 8 y + z = x ⋯ ( 2 ) x + 5 8 y = y ⋯ ( 3 ) 1 4 y = z ⋯ ( 4 ) Consider equation ( 3 ) , x = y − 5 8 y x = 3 8 y Consider equation ( 4 ) , y = 4 z So,

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 9.2, Problem 13E

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The steady state vector of the matrix [018115800140].

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Chapter 9.2, Problem 12E

Chapter 9.2, Problem 14E

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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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The steady state vector of the matrix [ 0 1 8 1 1 5 8 0 0 1 4 0 ] .

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