Test_1_2000 - first ball drawn was black given that the...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 26, 2000 MIDTERM TEST 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. Results from the text need not be reproduced in detail - you can merely cite the source. (25) 1. An urn contains b black balls and r red balls. One of the balls is drawn at random, but when it is put back in the urn c additional balls of the same color are put in with it. Now suppose that we draw another ball. Find the probability that the
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Unformatted text preview: first ball drawn was black given that the second ball drawn was red. (25) 2. Suppose the random variables X, Y, Z have the following joint p.d.f.: Determine the univariate marginal p.d.f. for each of X, Y, and Z. (25) 3. Consider two random variables X and Y, where X = price and Y = quantity. Researcher A predicts quantity given price with E*(Y|X), making prediction error U = Y - E*(Y|X). Researcher B predicts price given quantity with E*(X|Y), making prediction error V = X - E*(X|Y). Find Cov(U, V) and express it in terms of the correlation D XY between price and quantity. (13) 4. (a) Exercise 3.4.11(b) (12) (b) Using Exercise 3.4.11(c), do Exercise 3.4.11(d)....
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