Exam2_2008 - Question 2 a Find an Inverse Transform...

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Name______________________________ IE 305 Exam 2 * Spring 2008 * Packard 416 * 10:10 to 11:00 * April 14 Instructions 1. There are 4 questions, each worth 25 points. 2. The test is open book, open notes 3. You must show all relevant work to receive credit 4. Exam may be “long”, so don’t waste too much time on any one problem 5. Unless stated otherwise, you should assume α = 0.05 The Rayleigh Distribution In this exam we will use the Rayleigh distribution in many of the problems. This distribution was named for the famous Physicist Lord Rayleigh, and is used in many applications including bomb siting and wind speed modeling. This distribution has a single parameter, γ . The density, CDF, and expected value of the Rayleigh distribution are: γ π 4 ) ( 0 1 ) ( 0 2 ) ( 2 2 = - = = - - x E x for e x F x for xe x f x x
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Question 1. Consider the random number generator given by: X 0 =11, X i+1 =35X i @128. a) Use this generator to generate 5 observations of a Uniform(0,1) distribution. b) What will the period of this random number generator be?
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Unformatted text preview: Question 2. a) Find an Inverse Transform Algorithm for generating observations from the Rayleigh Distribution. b) Given the 5 Uniform(0,1) values from question 1, use the method in part a) of this question to generate 5 observations on the Rayleigh distribution with γ =1 Question 3. a) Construct a PP plot for the 5 Rayleigh data points you generated in question 2, part b) to see if the Rayleigh distribution with γ =1 is a good fit. b) Do a Kolmogorov-Smirnov goodness of fit test to see if 5 Rayleigh data points you generated in question 2, part b) can be considered to come from a Rayleigh distribution with γ =1. Question 4. a) Find the Method of Moments estimator of the parameter γ of the Rayleigh distribution b) Find the Maximum Likelihood Estimator of the parameter γ of the Rayleigh distribution....
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Exam2_2008 - Question 2 a Find an Inverse Transform...

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