CS 7880 : Algorithmic Power Tools Scribe : Eric
نویسنده
چکیده
As with the tail bounds we saw in the last lecture, Chernoff’s formula is used to bound the probability that a random variable deviates from its mean. For this bound, however, the random variable under consideration will have a very specific structure. Let X1, . . . , Xn be independent {0, 1}-valued random variables, and define pi = Pr[Xi = 1] = E[Xi]. Then, X = ∑ iXi will be the random variable we study. Note that E[X] = E [ ∑ iXi] = ∑ i pi by linearity of expectations; we will denote this value by μ.
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