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Department of EconomicsProfessor Dale J. PoirierUniversity of California, IrvineDecember 5, 2006FINAL EXAMECON 220AStatistics and Econometrics I(open book)Directions: You must answer each of the following questions. Points (out of 100) are allocatedas noted to the left of each question. Allocate your time according to these points. To receive anypartial credit, you mustshow your work.(20)1.Consider a random sample Yt(t = 1, 2, ..., T) from a N(:, F2) distribution with unknownmean and variance. Also consider the following loss function for estimating F2:Finally, consider estimators of the form for some constant d, where S2is theusual unbiased estimator of F2. Find the value of d which minimizes risk.(20)2.Consider a random sample Yt(t = 1, 2, ..., T) from the gamma distribution G(", $). Finda method of moments estimator of "and $.3.Suppose the opening prices per share X1and X2of two similar stocks are independentrandom variables with common density fX(x) = ½ exp[-½(x-4)], 4 < x <
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