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Unformatted text preview: sition matrix for the chain. (b) Suppose the driver begins at the airport at time 0. Find the probability for each of his three possible locations at time 2 and the probability he is at hotel B at time 3. 1.7. Suppose that the probability it rains today is 0.3 if neither of the last two days was rainy, but 0.6 if at least one of the last two days was rainy. Let the weather on day n, Wn , be R for rain, or S for sun. Wn is not a Markov chain, but the weather for the last two days Xn = (Wn 1 , Wn ) is a Markov chain with four states {RR, RS, SR, SS }. (a) Compute its transition probability. (b) Compute the two-step transition probability. (c) What is the probability it will rain on Wednesday given that it did not rain on Sunday or Monday. 1.8. Consider the following transition matrices. Identify the transient and recurrent states, and the irreducible closed sets in the Markov chains. Give reasons for your answers. (a) 1 1 .4 2 0 3 .5 4 0 5 0 2 .3 .5 0 .5 .3 3 .3 0 .5 0 0 4 0 .5 0 .5 .3 5 0 0 0 0 ....
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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