Random variables, expectation and discrete distributions

Jacob Bernoulli spent years on the book that would found the mathematics of repeated trials; Ars Conjectandi appeared in 1713, eight years after his death. Its trials with two outcomes, success or failure, are still called Bernoulli trials.

In 1837 Siméon Denis Poisson published the distribution that bears his name, for counts of rare events. In 1898 Ladislaus Bortkiewicz showed how well it fitted two decades of records of Prussian soldiers killed by horse kicks. Today the same formula models packets arriving at a router and calls reaching a help desk.