Brazilian Journal of Probability and Statistics, Vol. 35, No. 3 (2021), pp. 435-441 (7 pages) The aim of this note is to give an elegant proof of a result due to E. G. Olds which concerns the density ...

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 ...