Foundations of CS II

Probability, Statistics, and Algorithms

Lecture 15: Tail bounds

Posted by James on February 15, 2012

Hear are the slides. Reading assignment: BT, Section 5.1.

5 Responses to “Lecture 15: Tail bounds”

  1. Xin said

    I’m wondering is it possible that we can have a version of slides without those giant portraits of mathematicians removed. It seems they always cover a few important stuff.
    Thanks.

  2. Nat said

    In the second equation defining chernoff bounds, should that denominator in the exponential be 2, rather than 3? If not, why? These equations don’t make a whole lot of sense to me…

    • James Lee said

      The “3” is correct. Unfortunately, we don’t have time to go over the proof of the Chernoff bound in class. It’s based on the “method of Laplace transforms.” The bounds for the upper and lower tail are not symmetric because a Bin(n,p) random variable is not symmetry around its expectation. They come from an approximation to the true tail behavior. You can see all this discussed on wikipedia: http://en.wikipedia.org/wiki/Chernoff_bound

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