Test_1_2006 - i (i = 0, 1, 2, . ..). Define For all values...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 31, 2006 MIDTERM EXAM 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. (20) 1. A population of voters contains 40% Republicans and 60% Democrats. It is reported that 30% of the Republicans and 70% of the Democrats favor an election issue. A person chosen at random from this population is interviewed and found to favor the issue in question. Find the probability that this person is a Democrat. (20) 2. Let Y be an integer-valued random variable for which P(Y = i) = p
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Unformatted text preview: i (i = 0, 1, 2, . ..). Define For all values of t such that h(t) is finite. Find M k h(t) / M t k * t=1 and identify it. 2 (20) 3. Consider two random variables Y 1 and Y 2 with joint p.d.f.: (a) Find the value of c which makes this a p.d.f. (b) Find P(Y 1 # .75, Y 2 $ .50). (20) 4. Consider the random variable X with p.d.f. where " > 0, $ > 0, and B( " , $ ) is the beta function. Find the p.d.f. of Y = 1/(1 + X) and identify it. (20) 5. 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....
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Test_1_2006 - i (i = 0, 1, 2, . ..). Define For all values...

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