ECON
Test_1_2002

# Test_1_2002 - Department of Economics University of...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 29, 2002 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. 1. Let X and Y be continuous random variables with p.d.f. f X,Y (x, y) = (6 - x - y)/8, if 0 < x < 2 and 2 < y < 4, and f X,Y (x, y) = 0, otherwise. (9) (a) Find f X (x). (9) (b) Find f Y|X (y). (9) (c) Find P(2 < Y < 3|X = 1). 2. Suppose Y and W are scalar random variables such that Y|W
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Unformatted text preview: θ , ω /w) and W γ (m, v), where θ , ω + , m + , and v + . Answer each of the following questions, fully justifying your answer in each case. (6) (a) Are Y and W independent? (6) (b) Is Y mean-independent of W? (6) (c) Is W mean-independent of Y? (6) (d) Are Y and W uncorrelated? (24) 3. Let Y 1 and Y 2 be random variables with the same variance, but possibly different means. Let Z 1 = Y 1 + Y 2 and Z 2 = Y 1- Y 2 . Find Cov(Z 1 , Z 2 ). (25) 4. Let X and Y be random variables. Define ε = Y - E(Y|X) and U = Y - E*(Y|X), where E(Y|X) is the population regression function and E*(Y|X) is its best linear predictor. Find Cov( ε , U)....
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