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Unformatted text preview: Economics 506 FALL 2009 FINAL EXAM Version A (Total Points: 200) Name: ___________________________________email:_______________________ 1) [Total points: 80] Consider the following density function = elsewhere , 1 ) ( 1 y e ry y f r y r where r is a known positive constant. a) [10 points] use the method of transformation to find the density function of U = Y r b) [10 points] Let Y 1 , Y 2 , , Y n denote a random sample from the density function given above. Find a sufficient statistics for . (Use the back side if you need to) 1 Economics 506 FALL 2009 FINAL EXAM c) [10 points] Use method of moment generating function to find the distribution of the sufficient statistics you found in part (b). d) [10 points] Let Y 1 , Y 2 , , Y n denote a random sample from the density function given above. Find the maximum likelihood estimator (MLE) of (Use the back side if you need to) 2 Economics 506 FALL 2009 FINAL EXAM e) [5 points] Is the MLE you found in part (d) a MVUE (minimum variance unbiased estimator) for ? f) [10 points] find the minimum variance of an unbiased estimator of , using Rao Cramer inequality. Confirm that it is the same as the variance of the MLE you found in part (d). (Use the back side if you need to) 3 Economics 506 FALL 2009 FINAL EXAM g) [15 points] s uppose r = 1 . Assume we take a sample of size 40 observations and find out that = = 40 1 160 i i y . Use the NeymanPearson lemma to find the most powerful test of ....
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This note was uploaded on 04/13/2011 for the course ECON 506 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 Economics

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