# t2 - Stat 5102 Second Midterm Exam April 8, 2009 Name...

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Stat 5102 Second Midterm Exam April 8, 2009 Name Student ID The exam is closed book and closed notes. You may use one 8 1 2 × 11 sheet 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 100. There are 6 pages and 5 prob- lems. 1. [20 pts.] Suppose X 1 , ... , X n are IID Gam( α,λ ), where α is known and λ is unknown. (a) Find the log likelihood for λ . (b) Find the maximum likelihood estimate (MLE) for λ . 1

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hood. (d) Find the expected Fisher information for λ . 2. [20 pts.] Suppose X 1 , ... , X n are IID having PDF f θ ( x ) = θx θ - 1 , 0 < x < 1 where θ > 0 is an unknown parameter. (a) Find the log likelihood for
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## This note was uploaded on 10/28/2010 for the course STAT 2102 taught by Professor Geyer during the Spring '09 term at Minnesota.

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t2 - Stat 5102 Second Midterm Exam April 8, 2009 Name...

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