Notes on Feige's gumball machines problem
classification
🧮 math.PR
keywords
casefeigeconjecturedetaileddistributeddistributionsexceedsgeneral
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We give a detailed proof, in the identically distributed case, of a conjecture of Feige about the maximum probability that the sum of n independent non-negative integer valued random variables, each of mean 1, exceeds n. The general case is reduced to two-point distributions.
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