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10SimHw3

# 10SimHw3 - IEOR 4404 Simulation Prof Mariana...

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IEOR 4404 Assignment #3 Simulation February 14, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #3 – due February 19th, 2010 1. A pair of dice are to be continually rolled until all the possible outcomes 2, 3,. . . , 12 have occurred at least once. Develop a simulation study to estimate the expected number of dice rolls that are needed. 2. Use simulation to approximate cov( U,e U ), where U is uniform on (0,1). Compare your approximation with the exact answer. 3. For the acceptance-rejection algorithm for continuous random variables ﬁnd the distribution of the number of ( Y,U ) pairs that are rejected before acceptance occurs. What is the expected number of rejections? 4. In each of the following cases, give an algorithm that uses exactly one random number for generating a random variate with the same distribution as X . (a) X = min { U 1 ,U 2 } , where U 1 and U 2 are iid Uniform(0,1). (b)

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10SimHw3 - IEOR 4404 Simulation Prof Mariana...

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