A stronger form of the Chebyshev inequality. Let X1, X2,…, Xn be independent random variables with finite expectations and variances. Define the partial sum Sk by . The inequality states that, for all positive values of ɛ,, where, for each k, μk and σk2 are, respectively, the expectation and variance of Sk. See also Bernstein inequality; Hölder inequality; Markov inequality; Minkowski inequality.
Subjects: Probability and Statistics.