Explanation Given: The current market shares of the three major automobile manufacturers, A , B , and C in a certain country are 60 % , 30 % and 10 % , respectively. Of the customers who bought a car manufactured by A , 75 % would again buy a car manufactured by A , 15 % would buy a car manufactured by B , and 10 % would buy a car manufactured by C . Of the customers who bought a car manufactured by B , 90 % would again buy a car manufactured by B , whereas 5 % each would buy cars manufactured by A and C . Of the customers who bought a car manufactured by C , 85 % would again buy a car manufactured by C , 5 % would buy a car manufactured by A , and 10 % would buy a car manufactured by B . Approach: Enter the matrix X 0 as the matrix A and the matrix T as the matrix B in B ^ 5 * A to calculate X 5 . Calculation: Let the automobile manufacturers A , B , and C correspond to state 1 , state 2 , and state 3 of the Markov chain respectively. The initial probability distribution is given by, X 0 = A B C [ 0.6 0.3 0.1 ] The transition matrix associated with the problem is, T = A B C [ 0

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

11th Edition

ISBN: 9781305283831

Author: Tan

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 9.1, Problem 3TE

To determine

To find:

The market share that will be held by each manufacturer five model years after the study began, that is, X5.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 2TE

Chapter 9.1, Problem 4TE

Students have asked these similar questions

Your employer automatically puts 5 percent of your salary into a 401(k) retirement account each year. The account earns 10% interest. Suppose you just got the job, your starting salary is $60000, and you expect to receive a 2.5% raise each year. For simplicity, assume that interest earned and your raises are given as nominal rates and compound continuously. Find the value of your retirement account after 20 years

Compute the principal values of i¹² (i — 1)² and (i(i − 1))². - -

1 2 3 Consider the matrix A = 0 4 5. Give an example of 006 (a) a nonzero matrix B for which det(A + B) = det(A) + det(B); (b) a matrix C for which det(A+C)det(A) + det(C).

Chapter 9 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition

Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQ Ch. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

The market share that will be held by each manufacturer five model years after the study began, that is, X 5 .

Solution Summary: The author calculates the market share that will be held by each manufacturer five model years after the study began. The initial probability distribution is given by X_0=c

Videos

To find:

The market share that will be held by each manufacturer five model years after the study began, that is, X5.

Want to see the full answer?

Chapter 9 Solutions

The market share that will be held by each manufacturer five model years after the study began, that is, X 5 .

Solution Summary: The author calculates the market share that will be held by each manufacturer five model years after the study began. The initial probability distribution is given by X_0=c

Videos

To find: The market share that will be held by each manufacturer five model years after the study began, that is, X5.

Want to see the full answer?

Chapter 9 Solutions

To find:

The market share that will be held by each manufacturer five model years after the study began, that is, X5.