Explanation Given information: The provided expressions are, x n = [ 1 − ( r + s ) ] x n − 1 + r and y n = [ 1 − ( r + s ) ] y n − 1 + s Formula used: The 2 × 2 stochastic matrix can be written in the form as, A = [ 1 − s r s 1 − r ] Where, r and s are the numbers between 0 and 1. Therefore, the successive matrix of distribution can be written as, [ x n − 1 y n − 1 ] = A ⋅ [ x n − 1 1 − x n − 1 ] Proof: Since, it is known that, x n − 1 + y n − 1 = 1 Rewrite the above expression as, y n − 1 = 1 − x n − 1 Then, the above expression can be written as, [ x n − 1 y n − 1 ] = [ x n − 1 1 − x n − 1 ] Now, the successive matrix of distribution can be written as, [ x n − 1 y n − 1 ] = A ⋅ [ x n − 1 1 − x n − 1 ] Substitute the matrix of A in the above matrix as, [ x n − 1 y n − 1 ] = [ 1 − s r s 1 − r ] [ x n − 1 1 − x n − 1 ] Now, simplify as, [ x n − 1 y n − 1 ] = [ 1 − s r s 1 − r ] [ x n −

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 12, Problem 2P

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To proof: The xn=[1−(r+s)]xn−1+r and yn=[1−(r+s)]yn−1+s using the fact that xn−1+yn−1=1

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Chapter 12, Problem 1P

Chapter 12, Problem 3P

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Chapter 12 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 12.1 - Consider the difference equation...Ch. 12.1 - Prob. 2CYU Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - For each of the difference equations in Exercises...Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E

Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Population Decline Moldova has negative population...Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - 27. Credit Card Mr. Jones owes $1000 on a credit...Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.2 - Prob. 1CYU Ch. 12.2 - Prob. 2CYU Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - Prob. 27E Ch. 12.2 - Prob. 28E Ch. 12.3 - Parachuting A parachutist opens her parachute...Ch. 12.3 - Prob. 2CYU Ch. 12.3 - 3. Retirement Fund Upon retirement, a person...Ch. 12.3 - Each of the graphs in Fig. 14 comes from a...Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Each of the graphs in Fig. 14 comes from a...Ch. 12.3 - Prob. 6E Ch. 12.3 - Each of the graphs in Fig. 14 comes from a...Ch. 12.3 - Prob. 8E Ch. 12.3 - In Exercises 914, sketch a graph having the given...Ch. 12.3 - Prob. 10E Ch. 12.3 - In Exercises 914, sketch a graph having the given...Ch. 12.3 - Prob. 12E Ch. 12.3 - Prob. 13E Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - Prob. 19E Ch. 12.3 - Prob. 20E Ch. 12.3 - Prob. 21E Ch. 12.3 - Prob. 22E Ch. 12.3 - Prob. 23E Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.3 - Prob. 27E Ch. 12.3 - Prob. 28E Ch. 12.3 - Prob. 29E Ch. 12.3 - Prob. 30E Ch. 12.3 - Prob. 31E Ch. 12.3 - Prob. 32E Ch. 12.3 - In these exercises, find a difference equation...Ch. 12.3 - Prob. 34E Ch. 12.3 - Prob. 35E Ch. 12.3 - Prob. 36E Ch. 12.4 - Prob. 1CYU Ch. 12.4 - Prob. 2CYU Ch. 12.4 - Prob. 3CYU Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - 6. Find the monthly payment on a 25-year $38,000...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Prob. 13E Ch. 12.4 - In these exercises, use a table or graph of an...Ch. 12.4 - In these exercises, use a table or graph of an...Ch. 12.4 - Prob. 16E Ch. 12.5 - Glucose Infusion Glucose is being given to a...Ch. 12.5 - Light at Ocean Depths Sunlight is absorbed by...Ch. 12.5 - 1. Population Dynamics In a certain country with...Ch. 12.5 - Population Dynamics A small city with current...Ch. 12.5 - 3. Drug Absorption After a certain drug is...Ch. 12.5 - Elevation and Atmospheric Pressure The atmospheric...Ch. 12.5 - Spread of Information A sociological study was...Ch. 12.5 - Solution Concentration A cell is put into a fluid...Ch. 12.5 - Learning Curve Psychologists have found that in...Ch. 12.5 - Genetics Consider two genes A and a in a...Ch. 12.5 - Account Balance Thirty thousand dollars is...Ch. 12.5 - 10. Account Balance Rework Exercise 9, where...Ch. 12.5 - Prob. 11E Ch. 12.5 - Prob. 12E Ch. 12.5 - Prob. 13E Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - In these exercises, answer the questions by...Ch. 12.5 - Prob. 20E Ch. 12 - Explain how a sequence of numbers is generated by...Ch. 12 - Prob. 2FCCE Ch. 12 - Prob. 3FCCE Ch. 12 - Prob. 4FCCE Ch. 12 - Prob. 5FCCE Ch. 12 - Prob. 6FCCE Ch. 12 - Prob. 7FCCE Ch. 12 - Prob. 8FCCE Ch. 12 - Prob. 9FCCE Ch. 12 - Prob. 10FCCE Ch. 12 - Prob. 1RE Ch. 12 - Prob. 2RE Ch. 12 - 3. Account Balance How much money would you have...Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Population Dynamics The population of a certain...Ch. 12 - 8. Mortgage The monthly payment on a 30-year...Ch. 12 - Prob. 9RE Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 1P Ch. 12 - Prob. 2P Ch. 12 - Prob. 3P Ch. 12 - Prob. 4P Ch. 12 - Prob. 5P Ch. 12 - Prob. 6P Ch. 12 - Prob. 7P Ch. 12 - Prob. 8P Ch. 12 - Prob. 9P

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To proof: The x n = [ 1 − ( r + s ) ] x n − 1 + r and y n = [ 1 − ( r + s ) ] y n − 1 + s using the fact that x n − 1 + y n − 1 = 1

Solution Summary: The author explains that the 2times 2 stochastic matrix can be written in the form of A=left[cc1-s& r

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To proof: The xn=[1−(r+s)]xn−1+r and yn=[1−(r+s)]yn−1+s using the fact that xn−1+yn−1=1

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Chapter 12 Solutions