One Thousand Exercises in Probability: Third Edition
Geoffrey Grimmett, David StirzakerThis volume contains more than 1300 exercises in probability and random processes together
with their solutions. Apart from being a volume of worked exercises in its own right, it is also
a solutions manual for exercises and problems appearing in the fourth edition of our textbook
Probability and RandomProcesses, published by OxfordUniversity Press in 2020, henceforth
referred to as PRP. These exercises are not merely for drill, but complement and illustrate the
text of PRP, or are entertaining, or both. The current edition extends the previous edition by
the inclusion of numerous new exercises, and several new sections devoted to further topics
in aspects of stochastic processes. Since many exercises have multiple parts, the total number
of interrogatives exceeds 3000.
Despite being intended in part as a companion to PRP, the present volume is as self-
contained as reasonably possible. Where knowledge of a substantial chunk of bookwork is
unavoidable, the reader is providedwith a reference to the relevant passage in PRP. Expressions
such as ‘clearly’ appear frequently in the solutions. Although we do not use such terms in
their Laplacian sense to mean ‘with difficulty’, to call something ‘clear’ is not to imply that
explicit verification is necessarily free of tedium.
The table of contents reproduces that of PRP. The covered range of topics is broad,
beginning with the elementary theory of probability and random variables, and continuing,
via chapters on Markov chains and convergence, to extensive sections devoted to stationarity
and ergodic theory, renewals, queues, martingales, and diffusions, including an introduction
to the pricing of options. Generally speaking, exercises are questionswhich test knowledge of
particular pieces of theory, while problems are less specific in their requirements. There are
questions of all standards, the great majority being elementary or of intermediate difficulty.
We have found some of the later ones to be rather tricky, but have refrained from magnif