Explanation Given: The transition matrix where P, M, and U refer to small, medium, and large businesses. P M U A = P M U [ 0.415 0.526 0.059 0.175 0.655 0.170 0.061 0.520 0.419 ] Explanation: The long-range probabilties for the economical status for people can be computed as the equilibrium vector for the transition matrix A . A vector v is said to be an equilibrium vector for a transition matrix A , if the following condition holds: v A = v Let the vector v be defined as follows, so that the multiplication holds. [ v 1 v 2 v 3 ] Then, v A = v [ v 1 v 2 v 3 ] [ 0.415 0.526 0.059 0.175 0.655 0.170 0.061 0.520 0.419 ] = [ v 1 v 2 v 3 ] This gives rise to the following system of equations, 0.415 v 1 + 0.175 v 2 + 0.061 v 3 = v 1 0.526 v 1 + 0.655 v 2 + 0.520 v 3 = v 2 0.059 v 1 + 0.170 v 2 + 0.419 v 3 = v 3 This can be simplified to, − 0.585 v 1 + 0.175 v 2 + 0.061 v 3 = 0 0

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

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

Publisher: PEARSON

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Chapter 10.2, Problem 34E

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The percentage people classified as poor, middle-class, and upper-middle class in the long-run.

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Chapter 10.2, Problem 33E

Chapter 10.2, Problem 35E

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Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (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. Land Use In one state, a Board of Realtors...Ch. 10.1 - Business The change in the size of businesses in a...Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Housing Patterns In a survey investigating changes...Ch. 10.1 - Migration A study found that the way people living...Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.2 - Which of the following transition matrices are...Ch. 10.2 - Which of the following transition matrices are...Ch. 10.2 - Which of the following transition matrices are...Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Find the equilibrium vector for each transition...Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Find the equilibrium vector for each transition...Ch. 10.2 - Prob. 16E Ch. 10.2 - Find the equilibrium vector for each...Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Business and Economics Quality Control The...Ch. 10.2 - 26. 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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How can we calculate the expected total...Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Business and Economics 23. Solar Energy In...Ch. 10.3 - 24. Company Training Program A company with a...Ch. 10.3 - Contagion Under certain conditions, the...Ch. 10.3 - 26. Medical Prognosis A study using Markov chains...Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Gambler's Ruin (a) Write a transition matrix tor a...Ch. 10.3 - 32. Tennis Consider a game of tennis when each...Ch. 10.3 - Professional Football In Exercise 40 of the first....Ch. 10 - 1. If a teacher is currently ill, what is the...Ch. 10 - Prob. 2EA Ch. 10 - Prob. 3EA Ch. 10 - Prob. 4EA Ch. 10 - Prob. 5EA Ch. 10 - Prob. 6EA Ch. 10 - Prob. 7EA Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Prob. 8RE Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Prob. 12RE Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - Prob. 16RE Ch. 10 - Prob. 17RE Ch. 10 - Prob. 18RE Ch. 10 - Prob. 19RE Ch. 10 - Prob. 20RE Ch. 10 - Prob. 21RE Ch. 10 - Prob. 22RE Ch. 10 - Prob. 23RE Ch. 10 - Prob. 24RE Ch. 10 - Prob. 25RE Ch. 10 - In Exercises 23-26, use the transition matrix P,...Ch. 10 - Prob. 27RE Ch. 10 - Prob. 28RE Ch. 10 - Prob. 29RE Ch. 10 - Decide whether each transition matrix is regular....Ch. 10 - Prob. 31RE Ch. 10 - Prob. 32RE Ch. 10 - Prob. 33RE Ch. 10 - Prob. 34RE Ch. 10 - Prob. 35RE Ch. 10 - Find all absorbing states for each matrix. 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The percentage people classified as poor, middle-class, and upper-middle class in the long-run.

Solution Summary: The author explains that the long-range probabilities for the economic status for people can be computed as the equilibrium vector for a transition matrix A.

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The percentage people classified as poor, middle-class, and upper-middle class in the long-run.

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