351final2008 - Make sure that this examination has 13...

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Make sure that this examination has 13 numbered pages University of Regina Final Examination 200830 (December 12, 2008) Statistics 351 Intermediate Probability Name: Student Number: Instructor: Michael Kozdron Time: 3 hours Read all of the following information before starting the exam. You have 3 hours to complete this exam. Please read all instructions carefully, and check your answers. Show all work neatly and in order, and clearly indicate your final answers. Answers must be justified whenever possible in order to earn full credit. Unless otherwise specified, no credit will be given for unsupported answers, even if your final answer is correct. You may use standard notation; however, any new notations or abbreviations that you introduce must be clearly defined. Calculators are permitted; however, you must still show all your work. You are also permitted to have TWO 8.5 × 11 pages of handwritten notes (double-sided) for your personal use. Other than these exceptions, no other aids are allowed. Note that blank space is not an indication of a question’s difficulty. The order of the test ques- tions is essentially random; they are not intentionally written easiest-to-hardest. This test has 13 numbered pages with 11 questions totalling 150 points. The number of points per question is indicated. For questions with multiple parts, all parts are equally weighted. Fact : For λ > 0, the density of a random variable X Exp( λ ) is f X ( x ) = 1 λ exp n - x λ o , 0 < x < . Fact : For p > 0, the Gamma function is given by Γ( p ) = Z 0 x p - 1 e - x dx. Fact : You may find it useful to know that for any a > 0 integration-by-parts implies Z a 2 xe - ax dx = - axe - ax - e - ax . DO NOT WRITE BELOW THIS LINE Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 TOTAL
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Statistics 351 Final Examination 200830 Time: 3 hours – 1 – Name: Student No.: Section: 1. ( 28 points ) Suppose that a random vector ( X,Y ) 0 has joint density function f X,Y ( x,y ) = ± 10 xy 2 , if 0 < x < y < 1 , 0 , otherwise . (a)
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This note was uploaded on 03/26/2012 for the course STAT 351 taught by Professor Michaelkozdron during the Fall '08 term at University of Regina.

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351final2008 - Make sure that this examination has 13...

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