# stats150-6 - STAT 150 FINAL -SPRING 2007 Instructor: Steven...

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Sheet1 Page 1 STAT 150 FINAL -SPRING 2007 Instructor: Steven Evans Instructions: Each question is worth an equal amount. Explain carefully and completely what you are doing at each step in full s Quote any results that you use from class. NAME: SID: 1) 2) 3) 4) 5) 6) TOTAL 1) Let p be a probability distribution on the nonnegative integers such that i > 0 for all i. Write down the transition matrix of an irreducible, aperiodic, recurrent Markov chain on the nonnegative integers that has p as stationary probability distribution. s 2) Consider the Markov chain with the following transition matrix . . 00.50 0 00.5 0.25 0 0.25 0.25 0 0.25 00.500.50 0 0 0.25 0.25 0 0.25 0.25 0 0 0 0.5 0 0.5 0.25 0.25 0 0.25 0.25 0 BBBBB CCCCC

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Sheet1 Page 2 P = Show that this chain is irreducible and aperiodic, and find the stationary probability distribution of the chain by showing that th e is reversible. i 3) Consider a Yule process with immigration. This is a birth-and-death
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## This note was uploaded on 07/11/2009 for the course CEE cee taught by Professor Monteiro during the Fall '05 term at University of California, Berkeley.

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stats150-6 - STAT 150 FINAL -SPRING 2007 Instructor: Steven...

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