Explanation Given Information: The transition probability matrix P is given below, P = [ 0 0.5 0.5 0.5 0.5 0 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 given by, x + y + z + ⋯ = 1 [ x y z ⋯ ] P = [ x y z ⋯ ] The steady-state vector is then, v ∞ = [ x y z ⋯ ] Calculation: Consider the transition probability matrix as below and solve for steady-state vector, P = [ 0 0.5 0.5 0.5 0.5 0 1 0 0 ] Now, solve the system of equations given by, x + y + z = 1 And, [ x y z ] P = [ x y z ] [ x y z ] [ 0 0.5 0.5 0.5 0.5 0 1 0 0 ] = [ x y z ] The equations come from the above system are, x + y + z = 1 0.5 y + z = x 0.5 x + 0.5 y = y 0.5 x = z Rewrite the given equations in standard form as below, x + y + z = 1 − x + 0.5 y + z = 0 0.5 x − 0.5 y = 0 0.5 x − 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 32E

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

P=[00.50.50.50.50100]

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Chapter 8.7, Problem 31E

Chapter 8.7, Problem 33E

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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 0.5 0.5 0.5 0.5 0 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=[00.50.50.50.50100]

Want to see the full answer?

Chapter 8 Solutions

The steady-state distribution vector if a transition matrix P is, P = [ 0 0.5 0.5 0.5 0.5 0 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=[00.50.50.50.50100]

Want to see the full answer?

Chapter 8 Solutions

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

P=[00.50.50.50.50100]