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08SimHw11

# 08SimHw11 - probability 0 5 i 50 i = 1 20 Let X denote the...

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IEOR 4404 Assignment #11 Simulation December 8, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #11 – due December 12th, 2008 1. Fourteen cities, of roughly equal size, are chosen for a traffic safety study. Seven of them are randomly chosen, and in these cities a series of newspaper articles dealing with traffic safety are run over a 1-month period. The number of traffic accidents reported in the month following this campaign are as follows: Treatment group: 19 31 39 45 47 66 75 Control group: 28 36 44 49 52 72 72 Determine the exact p -value (using the recursion given in lecture 24) when testing the hy- pothesis that the articles have not had any effect. 2. Consider a system of 20 independent components, with component i being functional with
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Unformatted text preview: probability 0 . 5 + i/ 50, i = 1 ,..., 20. Let X denote the number of functional components. Use simulation to estimate the conditional probability mass function P ( X = i | X ≤ 5), i = 1 , 2 , 3 , 4 , 5. 3. A random selection of m balls is to be made from an urn that contains n balls, n i of which have color type i = 1 ,...,r , ∑ r i =1 n i = n . Let X i denote the number of withdrawn ball that have color type i . Give an eﬃcient procedure for simulating X 1 ,...,X r conditional on the event that all r color types are represented in the random selection. Assume that the probability that all color types are represented in the selection is a small positive number....
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