STAT 5102 Midterm: STAT 5102 UMN s09 Test 2
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The exam is closed book and closed notes. 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. , xn are iid gam( , ), where is known and. Is unknown. (a) find the log likelihood for . (b) find the maximum likelihood estimate (mle) for . 1 (c) show that your mle is the unique global maximizer of the log likeli- hood. (d) find the expected fisher information for : [20 pts. ] . , xn are iid having pdf f (x) = x 1, 0 < x < 1 where > 0 is an unknown parameter. (a) find the log likelihood for .
