# David Bellhouse

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Mathematics and Worldviews 1

Probability in the 18th Century

In the 18th century, there is a multidirectional interplay between theory and application of probability. Initially, mathematicians used games of chance as a model and then looked for applications of their results. Later in the century, application inspired theory. This happened in Britain with respect to finance (annuities and insurance) and in continental Europe for celestial mechanics. On the theory side of probability, important insights were made in the early 18th century concerning binomial outcomes that included early expressions of the law of large numbers, the normal approximation to the binomial, and a version of Bayes’ theorem for the prediction of future binomial outcomes. The later 18th century saw developments in probability models for continuous, rather than discrete, outcomes. Parallel to the normal approximation to the binomial, a normal approximation to the distribution of the sample mean of continuous measurements was obtained. From these developments emerged methods of estimation of the parameters describing these models. It is in this context that the method of least squares was developed. These important results were in many cases inspired by practical problems.

*David Bellhouse* is Professor Emeritus of Statistics at the University of Western Ontario. He holds a BA and MA from the University of Manitoba and a PhD from the University of Waterloo. He has published several research papers in the history of probability and statistics as well as two books: *Abraham De Moivre: Setting the Stage for Classical Probability and Its Applications* (2011) and *Leases for Lives: The Emergence of Actuarial Science in Eighteenth-Century England* (2017). He is an Honorary Member of the Statistical Society of Canada, an Honoured Alumnus of the Faculty of Science of the University of Manitoba, and a Fellow of the American Statistical Association. He has been awarded the Gold Medal for Excellence in Teaching by the University of Western Ontario. Professor Bellhouse is a former president of the Statistical Society of Canada and has served on the editorial boards of five statistical journals.