Test_1_2009 - (25 2 In a skiing competition a competitor's...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 27, 2009 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. (25) 1. Suppose 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
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Unformatted text preview: (25) 2. In a skiing competition, a competitor's overall time is found by adding his time X in the downhill section to his time Y in the slalom section. Downhill times have an expected value of 75 seconds with a standard deviation of 5 seconds. Slalom times have an expected value of 105 seconds with a standard deviation of 6 seconds. Overall times have a standard deviation of 11 seconds. Assuming quadratic loss, what is the optimal linear prediction of the expected overall time of a competitor who has recorded 70 seconds in the downhill section? 3. Let X and Y have p.d.f. (10) (a) Find c. (15) (b) Find Prob (X $ Y). (25) 4. Consider Example 2.4.2 on pp. 48-50 of the text. Consider the random variable Z = E(Y 1 * Y 2 ). Find its density function....
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