Kolmogorov inequality

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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.

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