Probability: An Introduction

by Geoffrey R. Grimmett, Dominic Welsh

This new undergraduate text offers a concise introduction to probability and random processes. Exercises and problems range from simple to difficult, and the overall treatment, though elementary, includes rigorous mathematical arguments. Chapters contain core material for a beginning course
in probability, a treatment of joint distributions leading to accounts of moment-generating functions, the law of large numbers and the central limit theorem, and basic random processes.

Genres: Mathematics, Textbooks, Reference

224 pages, Paperback

First published November 20, 1986

Reviews

[max · Rating 5 out of 5]

The best single introduction to probability for first or second year undergraduate students, especially on courses similar to a typical UK undergraduate maths degree.

[Madhusa K · Rating 5 out of 5]

I've got the 2nd edition but not too much has changed. Too many probability books emphasise intuition at the expense of rigour. If you are like me your first course in probability had more to do with dice rolls, card games and interpretive dances than real math. Sigma-fields? Measurable spaces? Limit Theorems? Those are empty abstractions just getting in the way of understanding real statistics! right? Wrong.

Hand-waving away all the rigour to explain the higher level concepts might make students feel smart when 99% of the problems you are given involve at most two random variables but once you start to see random vectors, series convergences, measure theoretic probabilities, random processes and martingales thrown around like candy it becomes evidently clear that all that intuition matters little when trying to the chapter starts starts to feel more like you are deciphering hieroglyphics.

This is not a book for the enthusiastic beginner . This is an introductory Probability book for people who are going to be taking Statistics heavy courses until they graduate or move on to grad school. Although this book starts with sigma-fields and measures it isn't by any means Measure Theoretic, but it does build up a good foundation on the notion of probability spaces so you aren't left confused and stranded when your higher level courses and books start to make extensive references to such material.

This book doesn't waste time teaching you how to count or asking you to calculate numerous tail probabilities; it assumes you can figure that much out on your own. This is a book for people want a rigorous, mathematical and principled introduction to Probability.

Great book. Loved it.