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Unformatted text preview: where " > 0 and $ > 0. B. Use change-of-variables. C. P(D) = 1 - P(D c ) D. Use iterated expectations. 2 (25) 1. Let A and B be two events in a sample space S. Prove P(A 1 B) $ 1 - P(A c ) - P(B c ). (25) 2. Let X and Y have joint density Find Cov(X, Y). 3. Let X and Y be two random variables such that X * Y = y -B(T, y) (i.e., Binomial) and Y -$ ( " , * ) (i.e., Beta). (10) (a) Find E(X). (15) (b) Find Var(X). (25) 4. Consider Example 2.4.2 on pp. 48-50 of the text. Consider the random variable Z = E(Y 1 * Y 2 ). Find its density function....
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- Fall '10
- Econometrics, Probability theory, probability density function, Dale J. Poirier, Department of Economics University of California, ECON 220A Statistics