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Test_2_2010

# Test_2_2010 - these variables are independent and uniformly...

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Department of Economics Professor Dale J. Poirier University of California, Irvine December 7, 2010 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. 1. Suppose the marginal distribution of the random variable N is Poisson with mean 2 , and that the conditional distribution of the random variable Y given N = n is Y * N = n - P 2 (2n). (10) (a) Find E(Y). (10) (b) Find Var(Y). (15) 2. A woman leaves for work between 8AM and 8:30AM and takes between 40 and 50 minutes to get there. Let the random variable X denote her time of departure ( measured as minutes past 8AM), and let the random variable Y denote the travel time. Assuming that

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Unformatted text preview: these variables are independent and uniformly distributed, find the probability that the woman arrives at work before 9AM. (15) 3. Consider a sequence {Y T } of random variables such that as T 64 . Find the asymptotic distribution of 2 4. Let Y t (t = 1, 2, . .., T) be a random sample from a population with p.d.f. (10) (a) Is a sufficient statistic for 2 ? (10) (b) Find a complete sufficient statistic for 2 . 5. Let Y t (t = 1, 2, . .., T) be a random sample from f(y t * 2 ) = 2y t / 2 2 , 0 < y t < 2 . (5) (a) Is an unbiased estimator of 2 ? (5) (b) Find . (5) (c) Find the Cramer-Rao lower bound. (5) (d) Compare your answers in (b) and (c). What do you conclude? (10) 6. Submit your Matlab Assignment....
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Test_2_2010 - these variables are independent and uniformly...

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