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Question 8

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. Specifically: 

 

→ If it is sunny on one day, it will be sunny the next day 1/5 of the time, and be cloudy the next day 2/5 of the time. 

→ If it is sunny on one day, it will be sunny the next day 3/5 of the time, and be cloudy the next day 1/5 of the time. 

→ If it is sunny on one day, it will be sunny the next day 3/5 of the time, and be cloudy the next day 1/5 of the time.

 

Using 'sunny', 'cloudy' and 'rainy' (in that order) as the states in a system, set up the transition matrix for a arkov chain to describe this system. 

Using your matrix to determine the probability that it will rain on Wednesday if it is sunny on Sunday. 

Solution

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