- linear algebra
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 1/2 of the time, and never be cloudy the next day
if it is cloudy on one day, it will be sunny the next day 1/3 of the time, and never be cloudy the next day
if it is rainy 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
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.
find matrix P and probability of rain on wednesday
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