Suppose that the weather can be only sunny or cloudy and the weather conditions on successive mornings form a Markov chain with stationary transition probabilities. Suppose also that the transition matrix is as follows:

a. If it is cloudy on a given day, what is the probability that it will also be cloudy the next day?
b. If it is sunny on a given day, what is the probability that it will be sunny on the next two days?
c. If it is cloudy on a given day, what is the probability that it will be sunny on at least one of the next three days?

Transcribed Image Text:

Sunny Cloudy 0.3 0.4 0.7 Sunny Cloudy0.6