# t3 - Stat 5101 Final Exam December 22, 2011 Name Student ID...

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Stat 5101 Final Exam December 22, 2011 Name Student ID The exam is closed book and closed notes. You may use three 8 1 2 × 11 sheets of paper with formulas, etc. You may also use the handouts on “brand name distributions” and Greek letters. Put all of your work on this test form (use the back if necessary). Show your work or give an explanation of your answer. No credit for numbers with no indication of where they came from. The points for the questions total to 200. There are 8 pages and 8 prob- lems. 1. [25 pts.] Suppose the conditional distribution of Y given X is Bin( n,X ), where n is a constant and X is a random variable having mean μ and variance σ 2 . (a) Find E ( Y ). (b) Find var( Y ). 1

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f ( x ) = c · 1 + x 2 1 + p | x | + x 2 + | x | 10 / 3 , -∞ < x < . (a) Show that there exists a constant c such that f is a PDF. (b) If X is a random variable having this PDF, for what positive real numbers β does E ( | X | β ) exist? 2
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## This note was uploaded on 02/07/2012 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.

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t3 - Stat 5101 Final Exam December 22, 2011 Name Student ID...

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