Computer algebra in probability and statistics

This paper discusses the uses of computer algebra within statistics and probability. A distinction is drawn between the use of computer algebra packages to support investigations, by performing calculations, ankl their use to implement structure; to build in elements of a theory (such as stochastic calculus or the Taylor string theory of Barndorff Nielsen and others) as a preliminary to research investigations. Brief surveys are given of instances in the literature of use of computer algebra in probability and statistics. Two examples of implementations of structure are discussed, both drawn from the author's own work with the computer algebra package REDUCE. One is a simple demonstration using moments of the Poisson distribution. The other is itovsn3 , an implementation of the semimartingale stochastic calculus. It is described how itovsn3 may be used to derive the characteristic function of the Lévy stochastic area, following a proof due to S. Janson. Prospects for future work and for work in progress are discussed.