Explanation Given Information: The transition probability matrix P is provided below: P = [ 0 1 0 1 3 1 3 1 3 1 0 0 ] Formula used: To calculate the steady-state probability vector for a Markov system for transition probability matrix P , solve the system of equations as: x + y + z + ⋯ = 1 [ x y z ⋯ ] P = [ x y z ⋯ ] The steady-state vector is, v ∞ = [ x y z ⋯ ] Calculation: Consider the transition probability matrix as below and solve for steady-state vector, P = [ 0 1 0 1 3 1 3 1 3 1 0 0 ] Now, solve the system of equations: x + y + z = 1 And, [ x y z ] P = [ x y z ] [ x y z ] [ 0 1 0 1 3 1 3 1 3 1 0 0 ] = [ x y z ] The equations come from the above system are: x + y + z = 1 y 3 + z = x x + y 3 = y y 3 = z Rewrite the above equations in standard form as below: x + y + z = 1 − x + y 3 + z = 0 x − 2 y 3 = 0 y 3 − z = 0 Now, solve these equations to get the value for x , y and z

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8.7, Problem 33E

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To calculate: The steady-state distribution vector if a transition matrix P is:

P=[010131313100]

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Chapter 8.7, Problem 32E

Chapter 8.7, Problem 34E

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Chapter 8 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 2E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 8E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 10E

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The steady-state distribution vector if a transition matrix P is: P = [ 0 1 0 1 3 1 3 1 3 1 0 0 ]

Solution Summary: The author explains how to calculate the steady-state distribution vector for a Markov system for transition probability matrix P.

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To calculate: The steady-state distribution vector if a transition matrix P is:

P=[010131313100]

Want to see the full answer?

Chapter 8 Solutions

The steady-state distribution vector if a transition matrix P is: P = [ 0 1 0 1 3 1 3 1 3 1 0 0 ]

Solution Summary: The author explains how to calculate the steady-state distribution vector for a Markov system for transition probability matrix P.

Videos

To calculate: The steady-state distribution vector if a transition matrix P is: P=[010131313100]

Want to see the full answer?

Chapter 8 Solutions

To calculate: The steady-state distribution vector if a transition matrix P is:

P=[010131313100]