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hw5_orie3510_s10

hw5_orie3510_s10 - ORIE3510 Introduction to Engineering...

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ORIE3510 Introduction to Engineering Stochastic Processes Spring 2010 Homework 5: Discrete Time Markov Chains Due 2:30pm, March 3, 2010 (drop box) Be sure to write your name and section number or day on your homework. In all questions, be sure to give the justification for your answers. There are 4 problems for 100 total points. Problem 1 (20 points) Suppose that a population consists of the same fixed number of genes in any generation. Call this number m . Each gene is one of two possible genetic types. If exactly i genes out of the m in any generation are of type 1, then the next generation will have j type 1 genes (and m - j type 2 genes) with probability m j i m j m - i m m - j for j = 0 , 1 , . . . , m . Let X n denote the number of type 1 genes in the n -th generation, and assume that X 0 = i . (a) Find E [ X n ]. (b) What is the probability that eventually all the genes will be type 1? Problem 2 (30 points) Harry has his eye on a comely young lady whom he originally spotted at a high cholesterol cooking course. During the course, however, Harry never had the courage to introduce himself as a famous

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hw5_orie3510_s10 - ORIE3510 Introduction to Engineering...

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