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*(yx, z) = $ x + ( z, E*(yx) = * x, and E*(zx) = 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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 Fall '10
 DaleJ.POIRIER
 Econometrics, Variance, Probability theory, Dale J. Poirier, Department of Economics University of California

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