Explanation Given: D = [ 0.3 0.7 ] ; P = [ 0.2 0.8 0.5 0.5 ] Explanation: The initial distribution, D , and the transition matrix, P , are provided. The distribution after the first experiment, D 1 , is the product of the initial distribution and the transition matrix. D 1 = [ 0.3 0.7 ] [ 0.2 0.8 0.5 0.5 ] = [ 0.41 0.59 ] The distribution after the two repetitions of P , D 2 , is the product of the distribution after the first occurrence of the experiment, D 1 , and the transition matrix. D 2 = [ 0.41 0.59 ] [ 0.2 0.8 0.5 0.5 ] = [ 0.377 0.623 ] The long-term distribution would correspond to the equilibrium vector. A vector v is said to be an equilibrium vector for a transition matrix P , if the following condition holds: v P = v Let the vector v be defined as follows, so that the multiplication holds. [ v 1 v 2 ] Then, v P = v [ v 1 v 2 ] [ 0.2 0.8 0.5 0.5 ] = [ v 1 v 2 ] Simplify the left-hand side to obtain, [ 0.2 v 1 + 0.5 v 2 0.8 v 1 + 0.5 v 2 ] = [ v 1 v 2 ] This gives rise to the following system of equations: 0

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10, Problem 23RE

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Chapter 10, Problem 22RE

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Chapter 10 Solutions

Finite Mathematics (11th Edition)

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