Probability and Statistics used to be married; then they separated; then they got divorced; now they hardly ever see each other. (That's a mischievous first sentence, but there is more than an element of truth in it, what with the subjects' having different journals and with Theoretical Probability's sadly being regarded by many – both mathematicians and statisticians – as merely a branch of Analysis.) In part, this book is a move towards much-needed reconciliation. It is written at a difficult time when Statistics is being profoundly changed by the computer revolution, Probability much less so.

This book has many unusual features, as you will see later and as you may suspect already! Above all, it is meant to be fun. I hope that in the Probability you will enjoy the challenge of some ‘almost paradoxical’ things and the important applications to Genetics, to Bayesian filtering, to Poisson processes, etc. The real-world importance of Statistics is self-evident, and I hope to convey to you that subject's very considerable intrinsic interest, something too often underrated by mathematicians. The challenges of Statistics are somewhat different in kind from those in Probability, but are just as substantial.

(a) For whom is the book written? There are different answers to this question. The book derives from courses given at Bath and at Cambridge, and an explanation of the situation at those universities identifies two of the possible (and quite different) types of reader.