08SimHw9 - IEOR 4404 Simulation Prof. Mariana...

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IEOR 4404 Assignment #9 Simulation November 21, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #9 – due November 25th, 2008 1. Five elements, numbered 1, 2, 3, 4, 5, are initially arranged in a random order (i.e., the initial ordering is a random permutation of 1, 2, 3, 4, 5). At each stage one of the elements is selected and put at the front of the list. That is, if the present order is 2, 3, 4, 1, 5 and element 1 is chosen, then the new ordering is 1, 2, 3, 4, 5. Suppose that each selection is, independently, element i with probability p i , where p 1 = 1 15 , p 2 = 2 15 , p 3 = 3 15 , p 4 = 4 15 , p 5 = 5 15 . Let L j denote the position of the j th element to be selected, and let L = 100 j =1 L j . We are interested in using simulation to estimate E [ L ]. (a) Explain how we could use simulation to estimate E [ L ]. (b) Compute E [ N i ], where N i is the number of times element i is chosen in the 100 selections. (c) Let
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08SimHw9 - IEOR 4404 Simulation Prof. Mariana...

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