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Bernoulli Numbers and Probability Distributions: Some Connections

The Article, Published by D. S Broca in The Mathematical Scientist, 36, 2011, 30-36, 2012

Bernoulli numbers are a remarkable sequence of rational numbers which find application in seemingly disparate areas of mathematics. In this paper the definition and basic properties of Bernoulli numbers are reviewed. These are then applied to computing the mean, variance, and shape characteristics of some well-known probability distributions.