Probability Inequalities for sums of Bounded Random Variables

  • Wassily Hoeffding
Part of the Springer Series in Statistics book series (SSS)


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 PrSESnt 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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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Wassily Hoeffding
    • 1
  1. 1.University of North CarolinaUSA

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