Bernoulli numbers and the probability of a birthday surprise

Details Bernoulli numbers and the probability of a birthday surprise Bernoulli numbers and the probability of a birthday surprise

2003-04-02

arxiv.org/abs/math/0304028v4

Discrete Applied Mathematics 127 (2003), 657--663

Mathematics

Numerical Analysis

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Scientific paper

10.1016/S0166-218X(02)00396-7

A birthday surprise is the event that, given k uniformly random samples from a sample space of size n, at least two of them are identical. We show that Bernoulli numbers can be used to derive arbitrarily exact bounds on the probability of a birthday surprise. This result can be used in arbitrary precision calculators, and it can be applied to better understand some questions in communication security and pseudorandom number generation.

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