Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it ismclear today. Also assume that these probabilities do not change if information ismalso provided about the weather before today. (i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. (ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix
Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it ismclear today. Also assume that these probabilities do not change if information ismalso provided about the weather before today. (i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. (ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 9EQ
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Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it ismclear today. Also assume that these probabilities do not change if information ismalso provided about the weather before today.
(i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather.
(ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix
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