Department of EconomicsProfessor Dale J. PoirierUniversity of California, IrvineDecember 8, 2009FINAL 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.1.Suppose that the random variables Y1and Y2have the joint density function f(y1, y2)= 3()/2, for 0 #y1#1 and 0 #y2#1.(5)(a)Are Y1and Y2exchangeable?(5)(a)Are Y1and Y2independent? (20)2.Suppose X1and X2are i.i.d. with p.d.f. Is W = Rn(X1)/Rn(X2) an ancillary statistic? 3.Let Yt(t =1, 2, ..., T) be i.i.d. N(2, 22 ), 2> 0. Denote the usual sample mean andvariance estimators by
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