An engineering professor acquires a new computer once every two years. The professor can choose from three models: M1, M2, and M3. If the present model is M1, the next computer can be M2 with probability 0.25 or M3 with probability 0.1. If the present model is M2, the probabilities of switching to M1 and M3 are 0.5 and 0.15, respectively. And, if the present model is M3, then the probabilities of purchasing M1 and M2 are 0.7 and 0.2, respectively. Represent the situation as a Markov chain and express the probabilistic activities in the form of transition matrix. Also, determine the probability that the professor will purchase the current model in 4 years.

An engineering professor acquires a new computer once every two years. The professor can choose from three models: M1, M2, and M3. If the present model is M1, the next computer can be M2 with probability 0.25 or M3 with probability 0.1. If the present model is M2, the probabilities of switching to M1 and M3 are 0.5 and 0.15, respectively. And, if the present model is M3, then the probabilities of purchasing M1 and M2 are 0.7 and 0.2, respectively. Represent the situation as a Markov chain and express the probabilistic activities in the form of transition matrix. Also, determine the probability that the professor will purchase the current model in 4 years.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Decision Theory in Operations Management

Decision theory, also known as the theory of choice, is a branch of statistics that deals with making decisions based on the probability of the occurrence of an event. The chief purpose of decision theory is to identify the best course of action for the company with maximum payoffs.

Question

An engineering professor acquires a new computer once every two
years. The professor can choose from three models: M1, M2, and
M3. If the present model is M1, the next computer can be M2 with
probability 0.25 or M3 with probability 0.1. If the present model is
M2, the probabilities of switching to M1 and M3 are 0.5 and 0.15,
respectively. And, if the present model is M3, then the probabilities
of purchasing M1 and M2 are 0.7 and 0.2, respectively. Represent the situation as a Markov chain and express the probabilistic
activities in the form of transition matrix. Also, determine the
probability that the professor will purchase the current model in 4
years.

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