Berry–Esséen theorem

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A theorem published in 1941 that concerns the distribution of the mean, , of n independent identically distributed random variables, X1, X2,…, Xn. The theorem requires that the expected values of Xj, Xj2, and | Xj |3 are finite and equal to 0, σ2, and τ, respectively. Denoting the distribution function of the standard normal distribution by Φ, the theorem states that there is a value c for which , for all a. The value of c is known to be less than 0.766.

Subjects: Probability and Statistics.

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