t2 - Stat 5102 Second Midterm Exam April 13, 2001 Name...

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Unformatted text preview: Stat 5102 Second Midterm Exam April 13, 2001 Name Student ID The exam is open book, including handouts. It is closed notes. You may use one 8 1 2 × 11 sheet of paper with formulas, etc. You may use a calculator. 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 2 pages and 5 prob- lems. 1. [20 pts.] Suppose X 1 , X 2 , ... are i. i. d. Beta( θ, 1), that is the densities are f ( x | θ ) = θx θ- 1 , < x < 1 , and suppose the prior distribution for θ is Exp( λ ), where λ is a hyperpa- rameter (a known constant). (a) Find the posterior distribution of θ . (b) Find the posterior mode of θ (note: mode , not mean or median). 2. [20 pts.] Suppose data X 1 , ... , X n are assumed to be i. i. d. with Normal( μ, 4), where μ is an unknown parameter. Suppose we want to do a Bayesian analysis with prior distribution for...
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This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Spring '02 term at Minnesota.

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t2 - Stat 5102 Second Midterm Exam April 13, 2001 Name...

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