Explanation Given: D = [ 0.8 0.2 ] ; P = [ 0.9 0.1 0.2 0.8 ] 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 = [ 0.8 0.2 ] [ 0.9 0.1 0.2 0.8 ] = [ 0.76 0.24 ] 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 = [ 0.76 0.24 ] [ 0.9 0.1 0.2 0.8 ] = [ 0.732 0.268 ] 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 followss, so that the multiplication holds. [ v 1 v 2 ] Then, v P = v [ v 1 v 2 ] [ 0.9 0.1 0.2 0.8 ] = [ v 1 v 2 ] Simplify the left hand side to obtain, [ 0.9 v 1 + 0.2 v 2 0.1 v 1 + 0.8 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 24RE

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Chapter 10 Solutions

Finite Mathematics (11th Edition)

Ch. 10.1 - Decide whether each matrix could be a...Ch. 10.1 - Decide whether each matrix could be a probability...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Decide whether each matrix could be a probability...Ch. 10.1 - Decide whether each matrix could be a...Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Decide whether each matrix could be a transition...Ch. 10.1 - Decide whether each matrix could be a...

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - In Exercises and 16, write each transition diagram...Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Find the first three powers of each transition...Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Insurance An insurance company classifies its...Ch. 10.1 - Insurance The difficulty with the mathematical...Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - 32. 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Quality Control Suppose improvements are made...Ch. 10.2 - (a) Dry Cleaning Using the initial probability...Ch. 10.2 - Mortgage Refinancing In 2009, many homeowners...Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Migration As we saw in the last section, a study...Ch. 10.2 - 36. Criminology A study male criminals in...Ch. 10.2 - Prob. 37E Ch. 10.2 - Prob. 38E Ch. 10.2 - Prob. 39E Ch. 10.2 - Prob. 40E Ch. 10.2 - Prob. 41E Ch. 10.2 - 42. 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