hw0 - EE 376A Information Theory Prof T Weissman Handout#1...

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

View Full Document Right Arrow Icon
EE 376A Handout #1 Information Theory Monday, January 04, 2010 Prof. T. Weissman NOT due Homework Set #0 Note: HW0 has NO effect on your grade of EE376A. There is no requirement to hand it in. Those are warm-up exercises in probability. However, we would like to hear your feedbacks. If you have some cute problems in probability, please share with us as well. 1. ( Independence ) (a) Let Z be a bernoulli random variables (r.v.) with parameter 1/2, (Bern(1/2)), i.e. P ( Z = 0) = 1 / 2, P ( Z = 1) = 1 / 2. Let X be a bernoulli random variables with parameter p and X is independent of Z . Show that the modulo 2 sum of X and Z is independent of X for any p value. (b) Let Z 1 ,...,Z n be independent Bern(1/2) r.v’s. Suppose ( X 1 ,...,X n ) is a random bi- nary sequence and independent of ( Z 1 ,...,Z n ). Let Y i = X i + Z i mod 2. What is the distribution of ( Y 1 ,...,Y n )? (c) Consider a more general case. Let Z be uniformly distributed over { 0 , 1 ,...,M - 1 } . X is independent of Z , with arbitrary probability mass function over { 0 , 1 ,...,M - 1 } . Show that the modulo M sum of X and Z is independent of X .
Image of page 1

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

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

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern