IEOR 4404Assignment #5SimulationOctober 5, 2006Prof. Mariana Olvera-CraviotoPage 1 of 1Assignment #5– due October 13th, 20061. (From Ross) Give a method for generating a random variable having density functionf(x) =ex/(e-1),0≤x≤12. (From Ross) Suppose that we want to generate a random variableXwhose density functionisf(x) =12x2e-xx >0by using the rejection method with an exponential density having rateλ(mean 1/λ). Findthe value ofλthat minimizes the expected number of iterations of the algorithm used togenerateX.(Hint:Recall that from Assignment #4 the expected number of rejections isc-1, so the expected number of iterations isc.)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 theamounts 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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