Assignment04Sol

Assignment04Sol - Columbia University IEOR 4404: Simulation...

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Columbia University IEOR 4404: Simulation Fall 2009 Solutions to Assignment 4 1. (Exercise 5.2) Let X denote the random variable with the given density function f ( x ). We use the acceptance-rejection method in order to gen- erate X . Note that f ( x ) 1 / 2 for all 2 x 6. Let Y be a random variable uniformly distributed on [2 , 6], with density g ( x ) given by g ( x ) = 1 4 for 2 x 6 . It follows that f ( x ) g ( x ) 2 for 2 x 6 . (1) With this, we can implement the acceptance-rejection method to generate X . The value of the constant c in the algorithm is given by c = 2 by (1). The steps of the algorithm are the following: STEP 1. Generate a random number U 1 , uniform on (0 , 1). Set Y = 4 * U 1 + 2 (this makes Y uniform on (2,6)). STEP 2. Generate a random number U 2 , uniform on (0 , 1). STEP 3. If U 2 f ( Y ) 2 g ( Y ) , set X = Y . Otherwise return to STEP 1. 2. (Exercise 5.4) We can use the inverse transform method. From the explicit
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Assignment04Sol - Columbia University IEOR 4404: Simulation...

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