5 - MIT OpenCourseWare http:/ocw.mit.edu 14.30 Introduction...

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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 #5 14.30 - Intro. to Statistical Methods in Economics Instructor: Konrad Menzel Due: Tuesday, March 31, 2009 Question One The convolution formula is a useful trick when we are interested in the sum or average of independent random variables. In the last problem set, we dealt with the random variable X, below. e-" forx > 0 f (4 = 0 forx<O Now, suppose that X = XI = X2 = . . . = Xkare independent, identically distributed random variables. 1. Using the convolution formula, determine the PDF of fi = ;(x1 + X2) Hint: Define Zl = X1 and Z2 = XI + X2 and then use the transformation method to get back to Y2 from 22. 2. Compute its expectation: E[Y2]. 3. Using the convolution formula, determine the PDF for & = ;(XI + + X3). Hint: Use the hint from part 1 to define Z3 = + + X3 and perform a convolution with Z2 to transform the problem into Z3.
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This note was uploaded on 01/30/2010 for the course STAT 430 taught by Professor Jones during the Fall '10 term at Napa Valley College.

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5 - MIT OpenCourseWare http:/ocw.mit.edu 14.30 Introduction...

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