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# Probability Inequalities for Sums of Bounded Random Variables

Wassily Hoeffding
Journal of the American Statistical Association
Vol. 58, No. 301 (Mar., 1963), pp. 13-30
DOI: 10.2307/2282952
Stable URL: http://www.jstor.org/stable/2282952
Page Count: 18
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## Abstract

Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for \$\Pr \{ S - ES \geq nt \}\$ depend only on the endpoints of the ranges of the summands and the mean, or the mean and the variance of S. These results are then used to obtain analogous inequalities for certain sums of dependent random variables such as U statistics and the sum of a random sample without replacement from a finite population.

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