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hw7 - 75 100 200 Once the 10000 sample runs have all been...

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IEOR 161 University of California, Berkeley Spring 2010 Homework 7 Due date: April 2 (in discussion session), 2010. The following are taken from “Introduction to Probability Models” by Sheldon Ross ( 9th Edi- tion ). 1. 5.67, 5.72 2. 4.2, 4.3, 4.8 3. Consider a birth-death process with p i,i +1 = u, p i,i - 1 = d, p i,i = 1 - u - d, for i 1 and p 0 , 1 = u, p 0 , 0 = 1 - u - d. Simulate 10000 sample paths of this Markov chain starting at x (0) = 0 with u = 0 . 35 ,d = 0 . 55. For each simulation run, record the state of the Markov chain at time t = 5 , 10 , 20 , 50
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Unformatted text preview: , 75 , 100 , 200. Once the 10000 sample runs have all been generated, plot histograms of the distribution of the state for each of these times. (Normalize the his-tograms so that they represent a probability mass function). Explain in words what these histograms represent. • Plot the histogram of a geometric random variable with success probability p = 1-( u/d ). How does this compare with the histograms you have just constructed? 1...
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