ee464_hw7

# ee464_hw7 - EE 464, Mitra Homework 7 Due Friday, March 13,...

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EE 464, Mitra Spring 2009 Homework 7 Due Friday, March 13, 2009, 9am 464 Box This problem set investigates tail inequalities, transforms and preliminaries for bivariate random variables. 1. Very Short Problems on Tail Inequalities: (a) Prove the generalization of the Chebyshev inequality: P [ | X - c | ≥ a ] E [ | X - c | n ] a n Note that c is an arbitrary real number, a > 0 and n is a positive integer. (b) Consider a positive random variable X with mean a , show that P £ X a / a (c) Consider the various bounds we have considered so far. If we simultaneously consider the moments in the following set, ' E [ X ] , E £ X 2 / , E £ X 3 / , E £ X 4 /“ , can we come up with a tighter bound? 2. Compare the Markov, Chebyshev and Chernoﬀ bounds for P [ X a ] for a uniform random variable on [0 ,b ] and Bernoulli random variable with parameter p . Plot and compare the bounds for diﬀerent values of a,b and p . 3. For a Laplacian random variable with parameter

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## This note was uploaded on 02/02/2010 for the course EE 464 taught by Professor Caire during the Spring '06 term at USC.

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ee464_hw7 - EE 464, Mitra Homework 7 Due Friday, March 13,...

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