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Unformatted text preview: ORIE 361/523 – Homework 2 Instructor: Mark E. Lewis due February 6, 2008 (drop box) 1. Consider a gene composed of d subunits, where d is some positive integer and each subunit is either normal or mutant in form. Consider a cell with a gene composed of m mutant subunits and (dm) normal subunits. Before the cell divides into two daughter cells, the gene duplicates. The corresponding gene of one of the daughter cells is composed of d units chosen from the 2m mutant subunits and the 2(dm) normal subunits. Suppose, we follow a fixed line of descent from a given gene. Let X be the number of mutant subunits initially present and { X n ,n ≥ 1 } , be the number present in the nth descendent gene. Then, { X n ,n ≥ 1 } is a Markov Chain. Give the state space and the transition matrix for this Markov Chain. 2. An individual possesses r umbrellas which he employs in going from his home to office, and vice versa. If he is at home (the office) at the beginning (end) of a day and it is raining, thenvice versa....
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 Spring '07
 LEWIS,M.
 Probability theory, Stochastic process, Markov chain, mutant subunits

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