KnowraChebyshev's inequalityLinked fromLinked fromThe 11 pages that link to Chebyshev's inequality, each with the reason it gives.All 11Broader topic 4Related 3Compared with 4Law of large numbersRelated: For independent observations with finite variance, it bounds errors in the sample average and yields a weak-law proof.Hölder's inequalityRelated: Moment bounds derived with Hölder can strengthen or generalize probability estimates.InequalityBroader topic: It shows how inequalities yield useful bounds even with limited distributional information.Markov's inequalityBroader topic: Applying Markov's inequality to squared deviations yields this stronger, centered bound.Chebyshev's sum inequalityCompared with: Despite the shared name, this probability bound is distinct from the sequence inequality.Concentration inequalityBroader topic: It strengthens the mean-only bound when variance is known.Pafnuty ChebyshevBroader topic: It converts limited information about a distribution into a general probability bound.Erdős–Kac theoremRelated: Moment and variance bounds help control contributions from primes outside the main range.Kolmogorov's inequalityCompared with: It bounds one fixed sum, while Kolmogorov's inequality handles every partial sum at once.Popoviciu's inequalityCompared with: Unlike Popoviciu's result, it uses variance to bound tail probabilities, not support to bound variance.68–95–99.7 ruleCompared with: It applies without normality but gives weaker bounds than the rule’s normal-specific percentages.