One Thousand Exercises in Probability

This third edition is a revised, updated, and greatly expanded version of previous edition of 2001. The 1300+ exercises contained within are not merely drill problems, but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the reader. A broad range of subjects is covered, including elementary aspects of probability and random variables, sampling, generating functions, Markov chains, convergence, stationary processes, renewals, queues, martingales, diffusions, Lévy processes, stability and self-similarity, time changes, and stochastic calculus including option pricing via the Black-Scholes model of mathematical finance.

The text is intended to serve students as a companion for elementary, intermediate, and advanced courses in probability, random processes and operations research. It will also be useful for anyone needing a source for large numbers of problems and questions in these fields. In particular, this book acts as a companion to the authors’ volume, Probability and Random Processes, fourth edition (OUP 2020).

Table of Contents

1 Events and their probabilities

2 Random variables and their distributions

3 Discrete random variables

4 Continuous random variables

5 Generating functions and their applications

6 Markov chains

7 Convergence of random variables

8 Random processes

9 Stationary processes

10 Renewals

11 Queues

12 Martingales

13 Diffusion processes

About the Authors

Professor Geoffrey Grimmett, Director of Research and Professor Emeritus of Mathematical Statistics, University of Cambridge, David Stirzaker, Professor Emeritus, Mathematical Institute, University of Oxford

Geoffrey Grimmett is Professor Emeritus of Mathematical Statistics at the University of Cambridge. Cambridge has been his base for pursuing probability theory and the mathematics of disordered systems since 1992. He was Master of Downing College, Cambridge from 2013-2018 and has been appointed Chair of the Heilbronn Institute for Mathematical Research from 2020

He has written numerous research articles in probability theory and statistical mechanics, as well as three research books. With David Stirzaker and Dominic Welsh respectively, he has co-authored two successful textbooks on probability and random processes at the undergraduate and postgraduate levels.

David Stirzaker was educated at Oxford University and Berkeley before being appointed as Fellow and Tutor in Applied Mathematics at St John’s College, Oxford. He is now an Emeritus Research Fellow at St John’s College, and an Emeritus Professor at the Mathematical Institute, Oxford.

He has written five textbooks on probability and random processes, two of them jointly with Geoffrey Grimmett. Most recently, (2015), he has written The Cambridge Dictionary of Probability and its Applications.