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Probability
4.2.5 Suppose that the weather on any day depends on the weather conditions during the previous 2 days. We form a Markov chain with the following states: State (S, S) if it was sunny both today and yesterday, State (S,C) if it was sunny yesterday but cloudy today, State (C,S) if it was cloudy yesterday but sunny today, State (C, C) if it was cloudy both today and yesterday, and transition probability matrix Today's state (S,S) (S, C) (C,S) (C,C) (S, S) 0.7 0.3 0 0 (S, C) 0 0 0.4 0.6 P = (C,S) 0.5 0.5 0 0 (C, C) 0 0 0.2 0.8 (a) Given that it is sunny on days 0 and 1, what is the probability it is sunny on day 5? (b) In the long run, what fraction of days are sunny?

4.2.5 Suppose that the weather on any day depends on the weather conditions during the previous 2 days. We form a Markov chain with the following states: State (S, S) if it was sunny both today and yesterday, State (S,C) if it was sunny yesterday but cloudy today, State (C,S) if it was cloudy yesterday but sunny today, State (C, C) if it was cloudy both today and yesterday, and transition probability matrix Today's state (S,S) (S, C) (C,S) (C,C) (S, S) 0.7 0.3 0 0 (S, C) 0 0 0.4 0.6 P = (C,S) 0.5 0.5 0 0 (C, C) 0 0 0.2 0.8 (a) Given that it is sunny on days 0 and 1, what is the probability it is sunny on day 5? (b) In the long run, what fraction of days are sunny?

A First Course in Probability (10th Edition)
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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4.2.5 Suppose that the weather on any day depends on the weather conditions during the previous 2 days. We form a Markov chain with the following states: State (S, S) if it was sunny both today and yesterday, State (S,C) if it was sunny yesterday but cloudy today, State (C,S) if it was cloudy yesterday but sunny today, State (C, C) if it was cloudy both today and yesterday, and transition probability matrix Today's state (S,S) (S, C) (C,S) (C,C) (S, S) 0.7 0.3 0 0 (S, C) 0 0 0.4 0.6 P = (C,S) 0.5 0.5 0 0 (C, C) 0 0 0.2 0.8 (a) Given that it is sunny on days 0 and 1, what is the probability it is sunny on day 5? (b) In the long run, what fraction of days are sunny?
Transcribed Image Text:4.2.5 Suppose that the weather on any day depends on the weather conditions during the previous 2 days. We form a Markov chain with the following states: State (S, S) if it was sunny both today and yesterday, State (S,C) if it was sunny yesterday but cloudy today, State (C,S) if it was cloudy yesterday but sunny today, State (C, C) if it was cloudy both today and yesterday, and transition probability matrix Today's state (S,S) (S, C) (C,S) (C,C) (S, S) 0.7 0.3 0 0 (S, C) 0 0 0.4 0.6 P = (C,S) 0.5 0.5 0 0 (C, C) 0 0 0.2 0.8 (a) Given that it is sunny on days 0 and 1, what is the probability it is sunny on day 5? (b) In the long run, what fraction of days are sunny?
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