Poisson was among the first to recognise and disseminate the key implications of Laplace's now-celebrated "Analytic Theory of Probabilities" (1812). Poisson was the first to teach Laplace's formulae in lectures at the Sorbonne in 1836, and this book is an account of those lectures, published the following year. It includes the first appearance of several key concepts, among them "random variable" and "distribution function".

Poisson also developed the concept of the Confidence Interval, which was used by Gavarret in the latter's 1840 treatise on the use of mathematical methods in medicine. It is notable that Poisson effectively chose a much more stringent confidence level - 99.5 per cent - than is currently used

(Summary by R A J Matthews 12 Feb 2019)