On maximal tail probability of sums of nonnegative, independent and identically distributed random variables
2017
Abstract
We consider the problem of finding the optimal upper bound for the tail probability of a sum of k nonnegative, independent and identically distributed random variables with given mean x. For k = 1 the answer is given by Markov's inequality and for k = 2 the solution was found by Hoeffding and Shrikhande in 1955.
We show that the solution for k = 3 as well as for general k, provided x <= 1/(2k - 1), follows from recent results of extremal combinatorics.