Suppose that the weather in a particular region behaves according to a Markov chain
Chapter 3, Problem 3.7.8(choose chapter or problem)
Suppose that the weather in a particular region behaves according to a Markov chain. Specifically, suppose that the probability that tomorrow will be a wet day is 0.662 if today is wet and 0.250 if today is dry. The probability that tomorrow will be a dry day is 0.750 if today is dry and 0.338 if today is wet. [This exercise is based on an actual study of rainfall in Tel Aviv over a 27-year period. See K. R. Gabriel and J. Neumann, A Markov Chain Model for Daily Rainfall Occurrence at Tel Aviv, Quarterly Journal of the Royal Meteorological Society, 88 (1962), pp. 9095.] (a) Write down the transition matrix for this Markov chain. (b) If Monday is a dry day, what is the probability that Wednesday will be wet? (c) In the long run, what will the distribution of wet and dry days be?
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