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10SimHw8

# 10SimHw8 - IEOR 4404 Simulation Prof Mariana...

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IEOR 4404 Assignment #8 Simulation March 24, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #8 – due April 2nd, 2010 1. To estimate a certain parameter θ , we generated 20 independent vales of a random variable having mean θ . If the successive values obtained were 102, 112, 131, 107, 114, 95, 133, 145, 139, 117 93, 111, 124, 122, 136, 141, 119, 122, 151, 143 how many additional random variables do you think we will have to generate if we want to be 99 percent certain that our final estimate of θ is correct to within ± 0 . 5? 2. To estimate E [ X ], X 1 , . . . , X 16 have been simulated with the following values resulting: 10, 11, 10.5, 11.5, 14, 8, 13, 6, 15, 10, 11.5, 10.5, 12, 8, 16, 5. Based on these data, if we want the standard deviation of the estimator of E [ X ] (the sample mean X ( n )) to be less than 0.1, roughly how many additional simulation runs will be needed? ( Hint: Show first that the variance of X ( n ) is σ 2 /n , where σ 2 = var( X ), and then approximate σ 2 ) 3. A small factory consists of a machining center and inspection station in series, as shown in the figure below. Unfinished parts arrive to the factory with exponential interarrival times having

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10SimHw8 - IEOR 4404 Simulation Prof Mariana...

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