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In: Statistics and Probability

It has been claimed that the best predictor of today’s weather is today’s weather. Suppose that...

It has been claimed that the best predictor of today’s weather is today’s weather. Suppose that in the town of Octapa, if it rained yesterday, then there is a 60% chance of rain today, and if it did not rain yesterday there is an 85% chance of no rain today.
a) Find the transition matrix describing the rain probabilities.
b) If it rained Monday, what is the probability it will rain on Wednesday?
c) If it did not rain Friday, what is the probability of rain on Monday?
d) Using the transition matrix from part a, find the steady-state vector. Use this to determine the probability that it will be raining at the end of time.

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