Test_2_2008 - has breast cancer? 3. Suppose Y = [Y 1 , Y 2...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 9, 2008 FINAL 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. (10) 1. Consider two events A and B with Prob(A) = 1/3 and Prob(B c ) = 1/4. Can A and B be disjoint? Explain. (20) 2. Suppose 1% of women over the age of 40 who participate in routine mammography screening have breast cancer, and that 80% of women with breast cancer have positive test results indicating breast cancer. Also assume 9.6% of women without breast cancer yield positive test results. If a woman has a positive test, then what is the likelihood she
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Unformatted text preview: has breast cancer? 3. Suppose Y = [Y 1 , Y 2 , . .., Y T ] N-N T ( : , E ), where E = (1 - " )I T + "4 T 4 T N and 4 T is a T×1 vector with each element equal to one and I T is the T×T identity matrix. (5) (a) For what values of " is * E * > 0? (15) (b) Is a mean-square consistent estimator of : ? Why or why not? 4. Consider a random sample Y t (t = 1, 2, . .., T) from a distribution with p.d.f.: where r > 0 is known and 2 is unknown. 2 (5) (a) Find the distribution of . (10) (b) Find the maximum likelihood estimator of 2 . (5) (c) Is an unbiased estimator of 2 ? (10) (d) Does achieve the Cramer-Rao lower bound in finite samples? (20) 5. Consider Question 1 of your computer homework assignment. Attach your answers to parts (g), (h), (i), and (j)....
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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_2_2008 - has breast cancer? 3. Suppose Y = [Y 1 , Y 2...

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