Explanation Approach: Use the given data to make a transition matrix and then find the steady state vector of the transition matrix. 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 given data, The transition matrix associated with the Markov chain is given by, T = [ 0.80 0.10 0.10 0.10 0.85 0.05 0.10 0.05 0.85 ] To compute the distribution for long run, Let, X = [ x y z ] Be a steady state vector associated with the Markov process, The condition T X = X translates into the matrix equation, [ 0.80 0.10 0.10 0.10 0.85 0.05 0.10 0.05 0.85 ] [ x y z ] = [ x y z ] Solve the above matrix equation, [ 0.80 x + 0.10 y + 0.10 z 0.10 x + 0.85 y + 0.05 z 0.10 x + 0.05 y + 0.85 z ] = [ x y z ] Equivalently, the linear system of equation for above matrix equation is,

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

11th Edition

ISBN: 9781305283831

Author: Tan

Publisher: Cengage Learning

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Chapter 9.2, Problem 24E

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The share of the audience each network will command in the long run when the initial distribution vector is X0=ABCCBSNBC[0.400.400.20].

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Chapter 9.2, Problem 23E

Chapter 9.2, Problem 25E

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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 share of the audience each network will command in the long run when the initial distribution vector is X 0 = ABC CBS NBC [ 0.40 0.40 0.20 ] .

Solution Summary: The author explains that the probability distribution percentage of share of audience in long run for ABC, CBS, and NBC is 33.33% each.

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The share of the audience each network will command in the long run when the initial distribution vector is X0=ABCCBSNBC[0.400.400.20].

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Chapter 9 Solutions