hw4 - EE 351K Probability Statistics and Random Processes...

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EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Shakkottai/Vishwanath { shakkott,sriram } @ece.utexas.edu Homework 4 (Due 03/02/2009) Problem 1 The runner-up in a road race is given a reward that depends on the difference between his time and the winner’s time. He is given 50 dollars for being zero to two minutes behind, 30 dollars for being two to ﬁve minutes behind, 10 dollars for being 5 to 10 minutes behind, and nothing otherwise. Given that the difference between his time and the winner’s time is uniformly distributed between 0 and 15 minutes, ﬁnd the mean and variance of the reward of the runner-up. Problem 2 Let X be a random variable with PDF f X ( x ) = ± 3 x 2 7 if 1 < x 2 0 otherwise. and let Y = X 2 . Calculate E [ Y ] and var ( Y ) . Problem 3 Let X be Gaussian with mean 3 and variance 5. Let Y = 2 X + 4 . (a) Calculate the PDF of Y . (b) Find P ( Y 0) . Problem 4

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This note was uploaded on 10/26/2009 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas.

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hw4 - EE 351K Probability Statistics and Random Processes...

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