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: a. 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 3/10 of the time
b. if it is cloudy on one day, it will be sunny the next day 1/10 of the time, and be cloudy the next day 2/5 of the time
c. if it is rainy on one day, it will be sunny the next day 3/10 of the time, and be cloudy the next day 3/10 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 Wednesday if it is sunny on Sunday.
P = [ 0 0 0
0 0 0
0 0 0]