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Lecture16 - Review for the Final Exam In the Land of Oz...

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Review for the Final Exam 11/29/2005
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In the Land of Oz example, change the transition matrix by making R an absorbing state. This gives P = R N S R 1 0 0 N 1 / 2 0 1 / 2 S 1 / 4 1 / 4 1 / 2 . Find the fundamental matrix N , and also Nc and NR . Interpret the results. 1
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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 percent went to Dartmouth, 20 percent to Harvard, and 10 percent to Yale. Then the Markov chain has the transition matrix P = H Y D H 1 0 0 Y . 3 . 4 . 3 D . 2 . 1 . 7 . Find the probability that the grandson of a man from Dartmouth went to Harvard. 2
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Consider the Markov chain with general 2 × 2 transition matrix P = 0 1 1 / 3 2 / 3 . Is P ergodic? Is P regular? If it is ergodic, find the fixed probability vector.
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