hw7_ee464

hw7_ee464 - EE 464, Mitra Homework 7 Due Friday, March 13,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

hw7_ee464 - EE 464, Mitra Homework 7 Due Friday, March 13,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online