Exam+1+-+2010

Exam+1+-+2010 - 2 3. Let X, Y and Z be three independent...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 19, 2010 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. 1. Let the density of X be unimodal and symmetric around zero with finite third moment. Define Y = X 2 . (5) (a) Find Cov(X, Y). (5) (b) Are X and Y independent? 2. Let X and Y be discrete random variables with joint and marginal probabilities given by x = -1 x = 0 x = 1 f Y (y) y = 0 1/6 0 1/6 1/3 y = 1 0 2/3 0 2/3 f X (x) 1/6 2/3 1/6 Answer each of the following. (7) (a) Is X statistically independent of Y? (6) (b) Is X mean-independent of Y? (6) (c) Is Y mean-independent of X? (6) (d) Are X and Y uncorrelated?
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Unformatted text preview: 2 3. Let X, Y and Z be three independent random variables distributed as (i = X, Y, Z). By taking functions (i.e., sums, differences, products, ratios, etc.) of these random variables, construct new random variables with the following distributions. (5) (a) N(0, 1) (5) (b) (5) (c) t 2 (5) (d) F 1,1 (5) (e) Cauchy 4. Consider a random sample of size T = 16 from a N( 2 , 11.25) distribution. Assume your prior beliefs are 2-N( , 11.25/ ), where = 1 and = 9. Finally, suppose the realized sample mean is = .25. (10) (a) Find the posterior density f( 2 * y). (10) (b) Find P( 2 > 0 * y). (10) (c) Find a .95 HPD interval for 2 . (10) (d) Consider the hypotheses H 1 : 2 # 1 and H 2 : 2 > 1. Find the posterior odds P(H 2 * y)/P(H 1 * y). 3 4...
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Exam+1+-+2010 - 2 3. Let X, Y and Z be three independent...

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