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Answers+Exam+1+-+2011 - Department of Economics University...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 18, 2011 ANSWERS TO EXAM 1 ECON 123A Econometrics I 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. (10) 1. Let A and B be two independent events with P(A) = 1/3 and P(B) = 1/4. Compute P(A c B). Solution: Pr(A c B) = P(A) + Pr(B) ! P(A 1 B) = P(A) + P(B) ! P(A) P(B) = 1/3 + 1/4 - 1/12 = ½. (15) 2. How well is your “gaydar” working? Let G denote the event that the sexual orientation of the person sitting next to you is “gay.” Assume 1/20 students are gay. Suppose the accuracy of your gaydar is such that you conclude (denoted +) the person is gay .70 of the time if they are in fact gay, and you mistakenly conclude they are gay .10 of the time when in fact they are not gay. If your gaydar tells you the person is not gay (denoted -), what is the probability the person is gay?
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