(c.) 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 is dear today. Also assume that these probabilities do not change if information is also 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 3.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 31E
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Cs401 3c

(c.) 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 is
dear today. Also assume that these probabilities do not change if information is
also provided about the weather before today.
(i) Explain why the stated assumptions imply that the Markovian property
holds for the evolution of the weather.
3
(ii) Formulate the evolution of the weather as a Markov chain by defining its
states and giving its (one-step) transition matrix
Transcribed Image Text:(c.) 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 is dear today. Also assume that these probabilities do not change if information is also provided about the weather before today. (i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. 3 (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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