Chap6_7_Review

# Chap6_7_Review - IE 305/404 Spring 2009 Review Questions...

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IE 305/404 Spring 2009 Review Questions for Exam 2 (ignore that we start at question 4) Question 4 (Chapter 7) In the table below is output from EXCEL for the random number generator: X i+1 = 59X i @ 512 X 0 = 73 i X(i) aX(i) aX(i)@M U(i) (2 digits) 0 73 4307 211 1 211 12449 161 0.41 2 161 9499 283 0.31 3 283 16697 313 0.55 4 313 18467 35 0.61 5 35 2065 17 0.07 6 17 1003 491 0.03 7 491 28969 297 0.96 8 297 17523 115 0.58 9 115 6785 129 0.22 10 129 7611 443 0.25 a) What will X 11 be? What will U 11 be? Explain or show work. X 11 = _____________ U 11 = _____________ b) What will X 128 be? What will U 128 be? Explain or show work. X 128 = ___________ U 128 = ___________ Question 5 (Chapter 6) Below is an actual plot of the empirical CDF of the 10 data points in question 1 along with the CDF for the U(0,1) distribution.

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 a) Perform the Kolmogorov-Smirnov Goodness of Fit Test at α=0.05 to test if the data comes from a U(0,1) distribution. b) Perform a Chi-Squared Goodness of Fit test at α=0.05 to test if the data comes from a U(0,1) distribution. Use 2 cells. c) Construct a P-P Plot for the 10 data points in question 1 to see if the data are from a U(0,1) distribution. Question 6 (Chapter 6) Below is a picture of the Uniform( θ -0.5 , θ +0.5) Distribution. You are given the following dataset of size 5 from this distribution: 0.6, 0.75, 1.1, 1.25, 0.9 a) Find a maximum likelihood estimator of θ . Be sure to show work and/or provide adequate explanation. b) Find the method of moments estimator of θ . Be sure to show work and/or provide adequate explanation. 1.0
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Chap6_7_Review - IE 305/404 Spring 2009 Review Questions...

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