hw6simu - = j ) = ± 1 2 ² j +1 + ( 1 2 ) 2 j-1 3 j , j =...

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IEOR 4404 Assignment #6 Simulation October 12, 2006 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #6 – due October 20th, 2006 1. (From Ross) Write a computer program that, when given a probability mass function { p j , j = 1 , . . . , n } as an input, gives as an output the value of a random variable having this mass function. 2. (From Ross) A deck of 100 cards— numbered 1,2,. .., 100— is shuffled and then turned over one card at a time. Say that a “hit” occurs whenever card i is the i th card to be turned over, i = 1 , . . . , 100. Write a simulation program to estimate the expectation and variance of the total number of hits. Run the program. Find the exact answers and compare them with your estimates. 3. (From Ross) Give an algorithm to generate the value of X , where P ( X
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Unformatted text preview: = j ) = ± 1 2 ² j +1 + ( 1 2 ) 2 j-1 3 j , j = 1 , 2 , . . . 4. (From Ross) Give an algorithm that generates a random variable having density f ( x ) = 30( x 2-2 x 3 + x 4 ) , ≤ x ≤ 1 Discuss the efficiency of this approach. 5. (From Ross) Buses arrive at a sporting event according to a Poisson process with rate 5 per hour. Each bus is equally likely to contain either 20, 21, . .., 40 fans, with the numbers in the different buses being independent. Write an algorithm to simulate the arrival of fans to the event by time t = 1. 6. (From Ross) Write a program that uses the thinning algorithm to generate the first 10 time units of a nonhomogeneous Poisson process with intensity function λ ( t ) = 3 + 4 t + 1...
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This note was uploaded on 11/17/2010 for the course IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

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