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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 #6 14.30 - Intro. to Statistical Methods in Economics Instructor: Konrad Menzel Due: Tuesday, April 7, 2009 Question One Let X be a random variable that is uniformly distributed on [ O , 1 ] (i.e. f (x) = 1 on that interval and zero elsewhere). In Problem Set #4, you use the "2-stepn/CDF technique and the transformation method to determine the PDF of each of the following transformations, Y = g(X). Now that you have the PDFs, compute (a) IE[g(X)], (b) g(IE[X]), (c) Var(g(X)) and (d) g(Var(X)) for each of the following transformations: 1. Y = xi, fY(y) = 4y3 on [O, 11 and zero otherwise. 2. Y = epX, fy(y) = on [a, l] and zero otherwise. 3. Y = 1 - e- X , fv(y) = -- 1 on [0,l 1-Y - ! ] and zero otherwise. 4. How does (a) IE[g(X)] compare to (b) g(IE[X]) and (c) Var(g(X)) to (d) g(Var(X)) for each of the above transformations? Are there any generalities that can be noted?
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