Test_2_2009 - and S 2 Note that and cS are unbiased...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 8, 2009 FINAL EXAM ECON 220A Statistics and Econometrics I (open book) Directions : You must answer each of the following questions. Points (out of 100) are allocated as noted to the left of each question. Allocate your time according to these points. To receive any partial credit, you must show your work. 1. Suppose that the random variables Y 1 and Y 2 have the joint density function f(y 1 , y 2 ) = 3( )/2, for 0 # y 1 # 1 and 0 # y 2 # 1. (5) (a) Are Y 1 and Y 2 exchangeable? (5) (a) Are Y 1 and Y 2 independent? (20) 2. Suppose X 1 and X 2 are i.i.d. with p.d.f. Is W = R n(X 1 )/ R n(X 2 ) an ancillary statistic? 3. Let Y t (t =1, 2, ..., T) be i.i.d. N( 2 , 2 2 ), 2 > 0. Denote the usual sample mean and variance estimators by
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