midterm1

midterm1 - ECON 139 Duke University Spring 2007 Midterm 1...

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ECON 139 Duke University Spring 2007 Midterm 1 Instructions (PLEASE READ CAREFULLY before starting): This test has a total of 4 problems and 70 points . You have 75 minute Remember to Show Your Work and please be sure that your handwriting is legible ! Be precise but brief. If a correct reply is hidden among wrong, or irrelevant, arguments, you will not get full credit. We will grade only what is written on your exam sheet. There should be plenty of space for all your calculations. There are two extra pages included at the end of the exam to be used as scratch paper. Do not turn in anything besides your exam sheet . Standard errors are in parentheses (unless otherwise noted). Name: TA: Section Day and Time: 1
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1. (12 points total) Consider the two random variables X and Y whose marginal distributions are given by X 2 4 6 8 10 Pr( X = x ) 1 = 4 3 = 8 1 = 8 1 = 8 1 = 8 and Y 1 1 Pr( Y = y ) 3 = 4 1 = 4 Assume X and Y are independent. a. (4 points) Construct the joint pdf for X and Y . b. (4 points) Compute the covariance of X and Y . 2
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How would the distribution of Y conditional on X = 2 di/er from the distribution of Y conditional on X = 6 3
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midterm1 - ECON 139 Duke University Spring 2007 Midterm 1...

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