STAT 5102 Midterm: STAT 5102 UMN Spring 10 Test 2
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The exam is closed book and closed notes. 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. Iid means independent and identically distributed; pdf means proba- bility density function; mle means maximum likelihood estimate. The points for the questions total to 100. There are 6 pages and 5 prob- lems: [20 pts. ] . , xn are iid n (0, ), where is an unknown parameter satisfying > 0. (a) find the log likelihood for . (b) find the mle for . 1 (c) show that your mle is a local maximizer of the log likelihood. , xn are iid having pdf f (x) = ( + 1)x 1(1 x),
