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Question 10 [10 points] The weather on any given day in a particular city can be sunny, cloudy, or rainy. It has been observed to be predictable largely on the basis of the weather on the previous day. Specfically: . if it is sunny on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time . if it is cloudy on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time . if it is rainy on one day, it will be sunny the next day 1/3 of the time, and be cloudy the next day 1/3 of the time Using 'sunny', 'cloudy', and 'rainy' (in that order) as the states in a system, set up the transition matrix for a Markov chain to describe this system. Find the proportion of days that have each type of weather in the long run. 3 P = 1 1 1 3 3 Sunny Proportion of days that are Cloudy 1I Rainy ooo