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Unformatted text preview: Stat 5102 Final Exam May 16, 2009 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 7 pages and 8 prob- lems. 1. [25 pts.] Suppose X 1 , ... , X n are independent and identically distributed (IID) Exp( λ ) and the prior distribution for λ is is Gam( α ,λ ), where α and λ are hyperparameters. (a) Find the posterior distribution for λ . (b) Find the mean of the posterior distribution for λ . 1 (c) Find the variance of the posterior distribution for λ . 2. [25 pts.] Find the Jeffreys prior for the Geo( p ) distribution. It is proper or improper?...
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- Spring '09
- Normal Distribution, pts, posterior distribution