ReviewQuestionsChap 8

# ReviewQuestionsChap 8 - Review Questions for Chapter 8 IE...

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Review Questions for Chapter 8 IE 305/404 Simulation Spring 2009 Question 1 Consider the following density function: ( 29 2 1 2 3 2 1 0 3 2 ) ( - = x for x x for x f a) Construct a composition algorithm to generate random variates from f(x) . b) Construct an inverse transform algorithm to generate random variates from f(x) . c) Construct a simple acceptance rejection algorithm to generate random variates from f(x) . d) Construct an acceptance rejection algorithm to generate random variates from f(x) . using the majorizing function t(x) = (2/3)*(2- x ). Question 2 a) Given the following two Uniform(0,1) random variates: U 1 = 0.45 and U 2 = 0.78, generate two N(0,1) random variates using the Box-Mueller method. b) Use the two Normal(0,1) random variates from part a) to generate a single observation from the Chi-Squared distribution with 2 degrees of freedom. c) Give an algorithm for generating from the truncated Exponential distribution with density function f(x) below: d) Give an algorithm for generating from the Double Exponential (a.k.a. LaPlace) distribution who’s density is given below: f ( x ) = 0.5 e -| x| for -∞≤ x ≤∞ 0 x f(x) 1 2 2/3

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Question 3 a) Develop an inverse transform method for generating random variates from the following density: f(x) = 1/3 0 x 1 f(x) = 2/3 1 x 2 f(x) = 0 elsewhere b) Use the following stream of U(0,1) random numbers to generate one observation using the algorithm you developed in part a): [0.07, 0.93, 0.54, 0.09, 0.89, 0.98, 0.57, 0.62] c) Develop a composition method to generate from the density in part a). d) Use the following stream of U(0,1) random numbers to generate one observation using
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## This note was uploaded on 04/26/2009 for the course IE 305 taught by Professor Storer during the Spring '08 term at Lehigh University .

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ReviewQuestionsChap 8 - Review Questions for Chapter 8 IE...

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