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Exam2_2009_Solutions

Exam2_2009_Solutions - NAME IE 305/404 Simulation Spring...

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NAME_______________________ IE 305/404: Simulation Spring 2009 Exam 2 Instructions Exam duration is 50 minutes, exam is open book, open notes, calculator is required. Sufficient work must be shown to receive partial credit. There are 5 questions, each question is worth 20 points. Exam seems long…don’t waste too much time on 1 question. 100's 00 90's 122233445557 80's 0001133334456688 70's 111112233455556677889 60's 0223334577899 50's 13556779 40's 33469 30's 57 Average 73.41772152 StDev 15.51889468 Median 75 N 79
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We will use the following distribution in several of the exam questions Consider a continuous random variable with density function, CDF, and expected value as shown below. Note that it has a single parameter μ . ) ln( 1 ) ( 1 ) ln( ln(x) ) ( 1 ) ln( 1 ) ( μ μ μ μ μ = = = X E x for x F x for x x f For μ =2 the density function looks like this: 0 0.5 1 1.5 0 1 2 3
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Question 1 (20 points) a) Consider the following linear congruential generator: X i+1 = (7X i +5)@100 with seed X 0 =14. Use it to generate 5 U(0,1) random variates. i X(i) ax+c X(i+1) U(i) 0 14 103 3 - 1 3 26 26 0.03 2 26 187 87 0.26 3 87 614 14 0.87 4 14 103 3 0.14 5 3 26 26 0.03 b) What is the period of this generator?
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