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C Secure https://lila1.lyryx.com/student-serviets/LabServlet?ccid 756 lyryX Homework 10 (Question 8) Name: Amrit Dhanjal Date: 2017-04-15 Question 8 [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 Spec fically: if it is sunny on one day, it will be sunny the next day 2/3 of the time, and be cloudy the next day 1/6 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. Use your matrix to determine the probability that it will rain on Thursday if it is sunny on Sunday. 0 0 0 0 0 0 0 0 0 Probability of rain on Thursday 0 Official Time: 20:40:28 SUBMIT AND MARK SAVE AND CLOSE

Explanation / Answer

The transition matrix P is:

To calculate the probability that it will rain on Thursday (today is Sunday), we will need to calculate P4.

The matrix P4 is:

Therefore, the probability that it will rain on Thursday if it is Sunny on Sunday = 0.2469.

(Note: Both matrices are 3x3 matrices).

Sunny Cloudy Rainy Sunny 2/3 1/6 1/6 Cloudy 1/3 1/3 1/3 Rainy 1/3 1/3 1/3

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