The Collected Works of Wassily Hoeffding pp 409-426 | Cite as

# Probability Inequalities for sums of Bounded Random Variables

Chapter

## 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*≥*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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© Springer Science+Business Media New York 1994