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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Recitation 16 (6.041/6.431 Spring 2007 Quiz 2) November 2, 2010 Problem 1: Xavier and Wasima are participating in the 6.041 MIT marathon, where race times are defined by random variables 1 . Let X and W denote the race time of Xavier and Wasima respectively. All race times are in hours. Assume the race times for Xavier and Wasima are independent (i.e. X and W are independent). Xaviers race time, X , is defined by the following density f X ( x ) = 2 c, if 2 x < 3 , c, if 3 x 4 , , otherwise , where c is an unknown constant. Wasimas race time, W , is uniformly distributed between 2 and 4 hours. The density of W is then f W ( w ) = braceleftbigg 1 2 , if 2 w 4 , , otherwise . (a) (i) Find the constant c (ii) Compute E [ X ] (iii) Compute E [ X 2 ] (iv) Provide a fully labeled sketch of the PDF of 2 X + 1...
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