Assuming that the climate in the city of Metepec behaves according to a Markov chain, consider the following data. The probability of rain on any following day is 70% if it rained the day before, and 20% if it did not rain the day before; Likewise, the probability that the next day will be dry is 80% if the day before was dry, and 30% if it rained the day before. From this information:  C. Find the probability that Friday is a dry day, given that it rained today, Tuesday. D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.7: Applications
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Assuming that the climate in the city of Metepec behaves according to a Markov chain, consider the following data. The probability of rain on any following day is 70% if it rained the day before, and 20% if it did not rain the day before; Likewise, the probability that the next day will be dry is 80% if the day before was dry, and 30% if it rained the day before. From this information:

 C. Find the probability that Friday is a dry day, given that it rained today, Tuesday.

D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today? 

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