Assuming that the weather in the city of Metepec behaves according to a Markov chain, consider the following data. The p

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Assuming That The Weather In The City Of Metepec Behaves According To A Markov Chain Consider The Following Data The P 1 (156.83 KiB) Viewed 157 times

Assuming that the weather 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 previous day, and 20% if it did not rain the previous day; likewise, the probability that the following day will be dry is 80% if the previous day was dry, and 30% if it rained the previous day. From this information: A. Construct a probability transition matrix, explain clearly what the rows and columns mean, as well as any entries in the matrix. B. Calculate the probability that it will rain tomorrow, given that it rained today, Tuesday. C. Calculate the probability that Friday will be a dry day, given that today, Tuesday, it rained. D. Suppose you want to calculate the probability that it will rain exactly six months from now, describe two different strategies you could employ to make this calculation would it really matter to consider what today's weather was? E. Choose one of the above strategies and calculate the probability that it will rain in six months.