Question: Problem 2 As you may have experienced yourselves, the weather in Clemson during winter time is not pleasant. We never have two nice days in

Problem 2 As you may have experienced yourselves, the weather in Clemson during winter time is not pleasant. We never have two nice days in a row. Consider three types of weather conditions: nice day, snow, and rain. If we do have a nice day today, then for the next day we are equally likely to have snow or rain. If we have snow or rain today, we have 50% chance having the same weather the next day; furthermore, if the weather next day changes from snow or rain, only half of the time is this a change to a nice day. (a) Formulate the weather condition in Clemson as a Markov chain. Clearly define the state space and one-step transition probability matrix. (b) Suppose it has been rainy for the past 5 days consecutively, what is the chance that it will be a nice day tomorrow? (Hint: this is an easy question, please don't over think!)

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