Test_1_2008 - has a standardized Cauchy distribution. 3....

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 28, 2008 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. Let X, Y and Z be random variables such that [Y, Z] N is independent of X. Show E(Y * X = x, Z = z) = E(Y * Z = z). (25) 2. Suppose X = [X 1 , X 2 ] N - N 2 ( : , G ), where Construct a random variable Y = Y(X 1 , X 2 ) which is a function of X 1 and X 2 and which
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Unformatted text preview: has a standardized Cauchy distribution. 3. Suppose X and Y have the joint p.d.f. f(x, y) = exp(-y), for 0 < x < y < 4 , and zero elsewhere. (5) (a) Are X and Y independent? (20) (b) Find Prob(X + Y < 1). 2 4. Let X denote consumption. Consider the constant relative risk aversion (CRRA) utility function Assume " 1. (10) (a) Let Z = R n(X). Denote its p.d.f. by f Z (z) = exp(z)f X [exp(z)] and its moment generating function by M Z (t) = E Z [exp(tZ)]. Assume M Z (t) exists at t = 1 - " . Express expected utility in terms of M Z ( @ ). (10) (b) Suppose Z -N( : , F 2 ). Find E[U(X)]. (5) (c) Suppose Z -t( 2 , * 2 , < ), where 0 < < < 4 . Find E[U(X)]....
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Test_1_2008 - has a standardized Cauchy distribution. 3....

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