Test_1_2003 - two flips and it shows tails. Now what is the...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 28, 2003 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 on the left. Allocate your time according to these points. To receive any partial credit, you must show your work. 1. A gambler has in his pocket one fair coin and one two-headed coin. (10) (a) He selects one of the coins at random, and when he flips it, it shows heads. What is the probability that it is the fair coin? (10) (b) Suppose that he flips the same coin a second time (independently of the first flip and again it shows heads. Now what is the probability that it is the fair coin? (10) (c) Suppose that he flips the same coin a third time (Independently of the first
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Unformatted text preview: two flips and it shows tails. Now what is the probability that it is the fair coin? (30) 2. Suppose that an automobile dealer pays an amount X 1 (in thousands of dollars) for a used car and then sells it for an amount X 2 (in thousands of dollars). Further suppose X 1 and X 2 have joint density and zero otherwise. Determine the dealers expected gain from the sale. 2 3. Let E**(Y * X) = X N $ ** be the best proportional predictor of Y given X, where $ ** is the constrained estimate of b in Theorem 2.7.7 which minimizes E( g 2 ) subject to a = 0. (10) (a) Show: $ ** = [E(XX N )]-1 E(XY). (10) (b) Let g ** / Y - X N $ **. Find E( g **). (10) (c) Find Cov(X, g **). (10) (d) Find E[( g **) 2 ]....
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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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Test_1_2003 - two flips and it shows tails. Now what is the...

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