# Notes on Feige's gumball machines problem - Mathematics > Probability

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Abstract: We give a detailed proof, in the identically distributed case, of aconjecture of Feige about the maximum probability that the sum of n independentnon-negative integer valued random variables, each of mean 1, exceeds n. Thegeneral case is reduced to two-point distributions.

Author: ** John H. Elton**

Source: https://arxiv.org/