Chernoff, Hoeffding, etc. bounds || @ CMU || Lecture 5c of CS Theory Toolkit

General statement of Chernoff and Hoeffding bounds, plus comments on negative association and the "Sampling Theorem" for estimating the mean of a random variable. Lecture 5c of "CS Theory Toolkit": a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University.
Resources for this lecture:
Chapter 2, "Basic tail and concentration bounds" of Wainwright's book "High dimensional statistics"
Dubhashi--Panconesi book "Concentration of measure for the analysis of randomized algorithms"
Mitzenmacher--Upfal book "Probability and computing"
McDiarmid's article "On the method of bounded differences"
Joag-Dev and Proschan's article "Negative association of random variables and applications"
Taught by Ryan O'Donnell (www.cs.cmu.edu...)
Course homepage on CMU's Diderot system: www.diderot.on...
Filmed by Cole H. for Panopto (www.panopto.com/)
Thumbnail photo by Rebecca Kiger (www.rebeccakph...)

[@hanmaslin]

Is there an error on the Hoeffding bound? Wikipedia has an extra factor of 2 outside the exponential.

[@alex_xiong]

The wiki page shows exactly the same bound Prof O'Donnell wrote: en.wikipedia.org/wiki/Chernoff_bound#Sums_of_independent_bounded_random_variables
could you share the link to the expression you saw?

[@hanmaslin]

@@alex_xiong en.wikipedia.org/wiki/Hoeffding%27s_inequality
Third expression in "Statement".