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.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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
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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