Department of EconomicsProfessor Dale J. PoirierUniversity of California, IrvineOctober 19, 2010EXAM 1ECON 123AEconometrics IDirections: You must answer each of the following questions. Points (out of 100) are allocated asnoted to the left of each question. Allocate your time according to these points. To receive anypartial credit, you must show your work.1.Let the density of X be unimodal and symmetric around zero with finite third moment.Define Y = X2.(5)(a)Find Cov(X, Y).(5)(b)Are X and Y independent?2.Let X and Y be discrete random variables with joint and marginal probabilities given byx = -1x = 0x = 1fY (y)y = 01/601/61/3y = 102/302/3fX (x)1/62/31/6Answer each of the following.(7)(a)Is X statistically independent of Y?(6)(b)Is X mean-independent of Y?(6)(c)Is Y mean-independent of X?(6)(d)Are X and Y uncorrelated?
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