One Thousand Exercises in Probability

Description

This volume of more than 1300 exercises and solutions in probability theory has two roles. It is both a freestanding book of exercises and solutions in probability theory, and a manual for students and teachers covering the exercises and problems in the companion volume Probability and Random Processes (4th edition).

• It includes worked solutions to all exercises and problems in the associated textbook. This is an invaluable handbook for students and teachers attending or giving courses in probability
• It contains more than 1300 exercises across a range of difficulty and topic. It is an essential aid for teachers compiling examinations and seeking exercises to illuminate lecture courses.

New to this edition

• The number of exercises and problems has been increased by around 300 to a total of about 1317
• There are sections on coupling from the past, Lévy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains

About the Author(s)

Professor Geoffrey Grimmett, Director of Research and Professor Emeritus of Mathematical Statistics, University of Cambridge, and Professor 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.

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

Reviews

"Review from previous edition "A useful source of exercises and problems from probability theory and random process. I have read it with great pleasure and can recommend it to students and teachers."" - EMS