Homework #3: Discrete Markov chains 1. In small town there are three different types of whether conditions: sunny day, rainy day, and windy day. A sunny day never happens two days in a row. If it is a sunny day, it is as likely to have a rainy day or windy day the next day. If it is a windy day or rainy day, it has an even chance of having the same conditions next day. For the other 50%, it is two times more likely to have a bad weather conditions than a sunny day. a) Draw a transition diagram. b) Is it an ergodic Markov chain (support your answer)? c) Obtain a transition probability matrix. d) What is the probability of having a sunny day 2 days from now, if today is a rainy day (Calculate without using matrix multiplication, hint: calculate just the needed value or matrix element)? e) What is the probability of having sunny 4 days from now, if today is a rainy day? f) What is the probability of having a rainy day 3 days from now if today is a windy day? g) Obtain the mean first passage time for all states.

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