Suppose that the weather in a particular region behaves according to a Markov chain. Specifically, suppose that

Question:

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.
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 of wet and dry days be?
Distribution
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