Probabilistic inequalities | Statistical inequalities

Boole's inequality

In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one of a countable number of events in terms of the individual probabilities of the events. Boole's inequality is named for its discoverer George Boole. Formally, for a countable set of events A1, A2, A3, ..., we have In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is σ-sub-additive. (Wikipedia).

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From playlist CS50 Sections 2015

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*** This is CS50, Harvard University's introduction to the intellectual enterprises of computer science and the art of programming. *** HOW TO SUBSCRIBE http://www.youtube.com/subscription_center?add_user=cs50tv HOW TO TAKE CS50 edX: https://cs50.edx.org/ Harvard Extension School: ht

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Related pages

George Boole | Subadditivity | Event (probability theory) | Probability theory | Finite set | Set (mathematics) | Inclusion–exclusion principle | Schuette–Nesbitt formula | Probability space | Probability measure | Pairwise independence | Fréchet inequalities