The minimum probability that a sum of independent nonnegative random variables falls below λ equals the smallest product over prefixes of (1 minus mean divided by remaining budget), proving Samuels' and Feige's conjectures.
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On Samuels' Conjecture
The minimum probability that a sum of independent nonnegative random variables falls below λ equals the smallest product over prefixes of (1 minus mean divided by remaining budget), proving Samuels' and Feige's conjectures.