10SimHw10 - IEOR 4404 Assignment #10 Simulation April 7,...

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Unformatted text preview: IEOR 4404 Assignment #10 Simulation April 7, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #10 due April 16th, 2010 1. In certain situations a random variable X , whose mean is known, is simulated so as to obtain an estimate of P ( X a ) for a given constant a . The raw simulation estimator from a single run is I , where I = ( 1 if X a if X a Because I and X are clearly negative correlated, a natural attempt to reduce the variance is to use X as a control and so use an estimator of the form I + c ( X- E [ X ]). (a) Determine the percentage of variance reduction over the raw estimator I that is possible (by using the best c ) if X were uniform on (0,1). (b) Repeat (a) if X were exponential with mean 1. (c) Explain why we knew that I and X were negatively correlated. 2. (a) Explain how control variables may be used to estimate = Z 1 e x 2 dx (this is the same of Problem 3 from Assignment #9)....
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This note was uploaded on 11/17/2010 for the course IEOR IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

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10SimHw10 - IEOR 4404 Assignment #10 Simulation April 7,...

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