Probability

Description

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields.

• Directed at first and second year undergraduates
• A concise introduction to probability
• An honest approach to mathematical rigour
• Careful choice of material, from probability to stochastic processes
• Enhanced by exercises and problems

New to this edition

• New chapter on Markov chains
• Has been developed in response to the evolution of course syllabuses
• Further examples, exercises, and problems including problems from the Oxford and Cambridge finals papers

About the Author(s)

Geoffrey Grimmett, Professor of Mathematical Statistics, University of Cambridge, and Dominic Welsh, Professor of Mathematics (retired), University of Oxford

Geoffrey Grimmett is Professor of Mathematical Statistics at the University of Cambridge and Master of Downing College, Cambridge. His research interests lie in disordered physical systems, including percolation and related processes. He has written numerous research articles in probability theory and statistical mechanics, as well as three research books and two successful textbooks on probability and random processes at the undergraduate and postgraduate levels.

Dominic Welsh is Professor Emeritus of Mathematics at the University of Oxford and Emeritus fellow of Merton College, Oxford. He held the John von Neumann Professorship at Bonn in 1990-91, and was appointed Professor of Mathematics at Oxford in 1993. His research interests include combinatorics and complexity theory, and he has written more than a hundred papers in these areas. He retired from Oxford University in 2005, and has since then held visiting positions in New Zealand and Barcelona.

Table of Contents

Part A BASIC PROBABILITY
1:Events and probabilities
2:Discrete random variables
3:Multivariate discrete distributions and independence
4:Probability generating functions
5:Distribution functions and density functions
PART B FURTHER PROBABILITY
6:Multivariate distributions and independence
7:Moments, and moment generating functions
8:The main limit theorems
9:Branching processes
10:Random walks
11:Random processes in continuous time
12:Markov chains