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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 s to °nish it. ° 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 . ° If time is running short, you should try to set up the problem without doing the °nal calculations. ° 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
c. (4 points) How would the distribution of Y conditional on X = 2 di/er from the distribution of Y conditional on X = 6 ? Explain, being speci°c about what those distributions are. 3

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2. (12 points total) Consider the random variable X . Assume that X i are iid with mean ° and you observe a random sample of size n > 20 . Consider the following estimators for
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midterm1 - ECON 139 Duke University Spring 2007 Midterm 1...

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