Probability: An Introduction

Paperback | September 21, 2014

byGeoffrey Grimmett, Dominic Welsh

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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 incognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations atCambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is anaccount of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time.This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

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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 incognate fields. It is suitable for a first c...

Geoffrey Grimmett is Professor of Mathematical Statistics at the University of Cambridge and Master of Downing College, Cambridge. His reserach 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 ...

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Format:PaperbackDimensions:288 pages, 9.69 × 6.73 × 0.7 inPublished:September 21, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198709978

ISBN - 13:9780198709978

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Table of Contents

Part A: BASIC PROBABILITY1. Events and probabilities2. Discrete random variables3. Multivariate discrete distributions and independence4. Probability generating functions5. Distribution functions and density functionsPart B: FURTHER PROBABILITY6. Multivariate distributions and independence7. Moments, and moment generating functions8. The main limit theorems9. Branching processes10. Random walks11. Random processes in continuous time12. Markov chains