# 4 - Fy(y = P[Y 5 y directly as we did in recitation You...

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MIT OpenCourseWare http://ocw.mit.edu 14.30 Introduction to Statistical Methods in Economics Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Problem Set #4 14.30 - Intro. to Statistical Methods in Economics Instructor: Konrad Menzel Due: Tuesday, March 17, 2009 Question One Suppose that the PDF of X is as follows: e-" forx > 0 f (4 = 0 f o r x 5 O 1. Determine the PDF for Y = Xi . 2. Determine the PDF for W = X : for k E N. Question Two Suppose that the PDF of a random variable X is as follows: L x f o r O < x < 5 f (4 = 0 otherwise Also, suppose that Y = X(5-X). Determine the PDF and CDF of Y. You can solve this in two ways. First, you can compute fy(y) using the formula given in class: taking care that g(x) is piece-wise monotonic. Second, you can solve this by finding
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Unformatted text preview: Fy(y) = P[Y 5 y] directly, as we did in recitation. You will receive extra-credit if you can do it both ways. Question Three (BainIEngelhardt , p. 226) (6 points) Let X be a random variable that is uniformly distributed on [O,1] (i.e. f (x) = 1 on that interval and zero elsewhere). Use two techniques from class ("2- stepn/CDF technique and the transformation method) to determine the PDF of each of the following: Question Four (BainIEngelhardt p. 227) If X N Binomial(n,p), then find the pdf of Y = n -X. Question Five (BainIEngelhardt p. 227) Let X and Y have joint PDF f (x,Y) = 4e-2(x+y) for 0 < x < 00 and 0 < y < co, and zero otherwise. 1. Find the CDF of W = X + Y . 2. Find the joint pdf of U = \$ and V = X. 3. Find the marginal pdf of U....
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