Stochastic

95 05 0 0 20 9 1 0 30 0 875 125 a suppose that a

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Unformatted text preview: s trying to decide if he wants to shave today. Suppose that Xn is a Markov chain with transition matrix 1 2 3 4 1 1/ 2 2/ 3 3/ 4 1 2 3 4 1 /2 0 0 0 1 /3 0 0 0 1/4 0 0 0 In words, if he last shaved k days ago, he will not shave with probability 1/(k+1). However, when he has not shaved for 4 days his mother orders him to shave, and he does so with probability 1. (a) What is the long-run fraction of time David shaves? (b) Does the stationary distribution for this chain satisfy the detailed balance condition? 69 1.12. EXERCISES 1.39. In a particular county voters declare themselves as members of the Republican, Democrat, or Green party. No voters change directly from the Republican to Green party or vice versa. Other transitions occur according to the following matrix: RDG R .85 .15 0 D .05 .85 .10 G 0 .05 .95 In the long run what fraction of voters will belong to the three parties? 1.40. An auto insurance company classifies its customers in three categories: poor, satisfactory and excellent. No one moves from poor to excellent or from excellent to poor...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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