10SimHw4 - IEOR 4404 Simulation Prof. Mariana...

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IEOR 4404 Assignment #4 Simulation February 20, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #4 – due February 26th, 2010 1. Let X be an exponential random variable with mean 1. Give an efficient algorithm for simulating a random variable whose distribution is the conditional distribution of X given that X < 0 . 05. That is, its density function is f ( x ) = e - x 1 - e - 0 . 05 , 0 < x < 0 . 05 Generate 1000 such variables and use them to estimate E [ X | X < 0 . 05]. Then determine the exact value of E [ X | X < 0 . 05]. 2. 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 #3 the expected number of rejections is c - 1, so the expected number of iterations is c .) 3. Write a computer program that, when given a probability mass function
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10SimHw4 - IEOR 4404 Simulation Prof. Mariana...

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