We prove the following inequality: for every positive integer n and every collection X 1 ; : : : ; X n of nonnegative independent random variables that each has expectation 1, the probability that their sum exceeds n+1 is at most < 1. Our proof produces a value of = 12=13 ' 0:923, but we conjecture that the inequality also holds with = 1 ? 1=e ' 0:632. 1 A… CONTINUE READING

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