Test_1_2007 - 2. Let X, Y and Z be random variables....

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 30, 2007 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. (10) 1. Consider a random variable X defined by Y = ln(X), where E(Y) = 0. Is E(X) greater than, less than, or equal to one?
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Unformatted text preview: 2. Let X, Y and Z be random variables. Consider the conditional density (10) (a) Find f(x * z) and state its support. (10) (b) Find f(y * x, z) and state its support. 3. Consider two random variables X and Y such that X -U(0, 1) and Y * X = x -N(x, x 2 ). Find: (10) (a) E(Y) (10) (b) Var(Y) (10) (c) Cov(X, Y) 2 4. Suppose the random variable Y has pfd (15) (a) Find E(Y). (15) (b) Find Var(Y). (10) 5. Suppose X 1 and X 2 are independent standard normal random variables. What is the distribution of Y = (X 1- X 2 ) 2 /2 ?...
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Test_1_2007 - 2. Let X, Y and Z be random variables....

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