Explanation Given Information: The provided regular stochastic matrix is [ .6 .5 .4 .5 ] . Formula used: If A is a regular stochastic matrix, then the stable distribution X is obtained from the solution of the linear equations, { sum of the entries of X = 1 A X = X Calculation: Consider the stable distribution, X = [ x y ] Then, the condition sum of the entries of X = 1 is represented by the equation, x + y = 1 Consider the regular stochastic matrix to be A . Then, the value of A is, A = [ .6 .5 .4 .5 ] The condition A X = X is represented by the equation, [ .6 .5 .4 .5 ] [ x y ] = [ x y ] Write the system from the matrix. { .6 x + .5 y = x .4 x + .5 y = y Then, the system of equations from the conditions X = 1 and A X = X is, { x + y = 1 .6 x + .5 y = x .4 x + .5 y = y Combine the terms in the second and third equations. { x + y = 1 − 0.4 x + 0.5 y = 0 0.4 x − 0 .5 y = 0 The second and third equations in the system are same, except for the multiplication of − 1 . So, omit the third equation 0.4 x − 0 .5 y = 0 . The system of equations becomes, { x + y = 1 − 0

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Author: Larry Goldstein, David Schneider

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Chapter 8, Problem 7RE

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Chapter 8, Problem 6RE

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Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

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The stable distribution of a regular stochastic matrix [ .6 .5 .4 .5 ] .

Solution Summary: The author calculates the stable distribution of a regular stochastic matrix left[cc.6&.5

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