Markov Chains: Project Problem Consider four wireless operators A, S, T, and V in a major metropolitan area. Suppose each of them offers incentives for consumers to sign annual contracts for their service. The probability of a consumer with company A staying with them after the contract expires is 60%, and switching to the other companies S, T, and V are 10%, 10%, and 20%, respectively. These probabilities for company S, T, and V are 20%, 50%, 10%, and 20% (i.e. 50% to stay with the same, 20%, 10%, and 20% probabilities switching to A, T, and V respectively); 20%, 15%, 50%, and 15%; and 15%, 10%, 15%, and 60%. Write a 4X4 stochastic matrix A for the problem scenario above.Suppose customer J signs a contract with company T in a given year. Write a vector corresponding to this customer JWhat is the probability that this customer stays with company T for a second year? The probability that customer J switches to company V?After five years, what are the probabilities that you will find customer J with each of these companies A, S, T, and VAfter 20 years, what are the probabilities that you will find customer J with each of these companies A, S, T, and VAre the probabilities in 4 and 5 the same?If the probabilities stopped changing, when did it first happen?

Answered: Consider four wireless operators A, S,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Markov Chains: Project Problem

Consider four wireless operators A, S, T, and V in a major metropolitan area. Suppose each of them offers incentives for consumers to sign annual contracts for their service. The probability of a consumer with company A staying with them after the contract expires is 60%, and switching to the other companies S, T, and V are 10%, 10%, and 20%, respectively. These probabilities for company S, T, and V are 20%, 50%, 10%, and 20% (i.e. 50% to stay with the same, 20%, 10%, and 20% probabilities switching to A, T, and V respectively); 20%, 15%, 50%, and 15%; and 15%, 10%, 15%, and 60%.

Write a 4X4 stochastic matrix A for the problem scenario above.
Suppose customer J signs a contract with company T in a given year. Write a vector corresponding to this customer J
What is the probability that this customer stays with company T for a second year? The probability that customer J switches to company V?
After five years, what are the probabilities that you will find customer J with each of these companies A, S, T, and V
After 20 years, what are the probabilities that you will find customer J with each of these companies A, S, T, and V
Are the probabilities in 4 and 5 the same?
If the probabilities stopped changing, when did it first happen?

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