Lecture14 - Absorbing Markov Chains 11/16/2005 More...

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Unformatted text preview: Absorbing Markov Chains 11/16/2005 More Examples of Markov Chains The President of the United States tells person A his or her in- tention to run or not to run in the next election. Then A relays the news to B, who in turn relays the message to C, and so forth, always to some new person. We assume that there is a probability a that a person will change the answer from yes to no when transmitting it to the next person and a probability b that he or she will change it from no to yes. We choose as states the message, either yes or no. The transition matrix is then P = yes no yes 1- a a no b 1- b . The initial state represents the Presidents choice. 1 More Examples ... In the Dark Ages, Harvard, Dartmouth, and Yale admitted only male students. Assume that, at that time, 80 percent of the sons of Harvard men went to Harvard and the rest went to Yale, 40 percent of the sons of Yale men went to Yale, and the rest split evenly between Harvard and Dartmouth; and of the sons of Dartmouth men, 70 per- cent went to Dartmouth, 20 percent to Harvard, and 10 percent to Yale. We form a Markov chain with transition matrix P = H Y D H 1 Y . 3 . 4 . 3 D . 2 . 1 . 7 ....
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Lecture14 - Absorbing Markov Chains 11/16/2005 More...

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