hw5 - IEOR 4404 Simulation Prof. Mariana Olvera-Cravioto...

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IEOR 4404 Assignment #5 Simulation October 5, 2006 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #5 – due October 13th, 2006 1. (From Ross) Give a method for generating a random variable having density function f ( x ) = e x / ( e - 1) , 0 x 1 2. (From Ross) Suppose that we want to generate a random variable X whose density function is f ( x ) = 1 2 x 2 e - x x > 0 by using the rejection method with an exponential density having rate λ (mean 1 ). Find the value of λ that minimizes the expected number of iterations of the algorithm used to generate X . ( Hint: Recall that from Assignment #4 the expected number of rejections is c - 1, so the expected number of iterations is c .) 3. (From Ross) A casualty insurance company has 1000 policyholders, each of whom will in- dependently present a claim in the next month with probability .05. Assuming that the amounts of the claims made are independent exponential random variables with mean $800, use simulation to estimate the probability that the sum of these claims exceeds $50,000.
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This note was uploaded on 11/17/2010 for the course IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

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