KnowraChernoff boundLinked fromLinked fromThe 10 pages that link to Chernoff bound, each with the reason it gives.All 10Broader topic 1Related 8Compared with 1Jensen's inequalityRelated: Convexity and expectation inequalities help convert exponential moments into tail bounds.Moment-generating functionRelated: Evaluating the function at a positive argument yields bounds on upper-tail probabilities.Markov's inequalityRelated: It strengthens basic expectation bounds when exponential moments are available.Chebyshev's inequalityCompared with: With stronger distributional information, it often gives exponentially tighter tails than Chebyshev's bound.Large deviation theoryRelated: It is a basic tool for deriving exponential estimates before sharper asymptotics.Concentration inequalityBroader topic: Exponential moments often yield sharp bounds for sums of independent variables.Hoeffding's inequalityRelated: Hoeffding’s inequality is obtained by optimizing a Chernoff bound.Condorcet's jury theoremRelated: It quantifies how quickly the chance of a mistaken majority can shrink.Azuma's inequalityRelated: Azuma's proof uses the same exponential-moment strategy, adapted to dependent increments.Boole's inequalityRelated: Probability proofs often combine concentration bounds with Boole's inequality across many events.