Test_1_2004 - (30) 2. Consider three random variable X, Y,...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 26, 2004 MIDTERM TEST ECON 220A Statistics and Econometrics I (open book) Directions : You must answer each of the following questions. Points are allocated as noted on the left. Allocate your time according to these points. To receive any partial credit, you must show your work. 1. Let X and Y be discrete random variables with joint and marginal p.m.f.s given below. x = -1 x = 0 x = 1 f Y (y) y = 0 1/6 0 1/6 1/3 y = 1 0 2/3 0 2/3 f X (x) 1/6 2/3 1/6 Answer each of the following. (5) a. Is X statistically independent of Y? (5) b. Is X mean-independent of Y? (5) c. Is Y mean-independent of X? (5) d. Are X and Y uncorrelated?
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Unformatted text preview: (30) 2. Consider three random variable X, Y, and Z such that E(X) = E(Y) = E(Z) = 0 and Also consider the linear projections: E*(y|x, z) = $ x + ( z, E*(y|x) = * x, and E*(z|x) = 8 x. Does * = $ + (8 ? (30) 3. Suppose Z = XY, where X and Y are independent random variables. Find an expression for in terms of : X , and : Y . 4. Let N (.) denote the standard normal p.d.f. . Consider two random variables X and Y with the joint p.d.f. f(x, y) = 2 N (x) N (y) for xy > 0, and f(x, y) = 0 for xy # 0. (10) a. Find the marginal p.d.f. of X and the marginal p.d.f. of Y. (10) b. Are X and Y independent?...
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This note was uploaded on 12/12/2010 for the course ECON ECON 220A taught by Professor Dalej.poirier during the Fall '10 term at UC Irvine.

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