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Probability: An Introduction

Geoffrey Grimmett and Dominic Welsh
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Peter Rabinovitch
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This book is an updated version of the 1986 classic that I learned from. There is a new chapter on Markov chains, and a few new sections and problems, but the book still retains its concise, direct style.

A few months ago I reviewed Blitzstein and Hwang’s excellent modern Introduction to Probability, which is chock full of features to ease the student’s path. How do they compare? The targets are the same — a first course in probability for students with calculus, but not measure theory. Both cover the basics: probabilities, random variables, discrete and continuous distributions, joint distributions, transformations, moments, conditioning, basic limit theorems, inequalities, and a chapter on Markov chains. Grimmett and Welsh add a chapter on branching processes, Blitzstein and Hwang add one on Markov Chain Monte Carlo.

The main difference is in how much they hold the students hand. Blitzstein and Hwang try everything possible to help the student understand the material. Grimmett and Welsh present the material unaided. Blitzstein and Hwang have problems with applications to just about anything you can think of (Google’s PageRank algorithm, legal, medical, ecology cryptography,genetics, computer science, etc), Grimmett and Welsh have only the typical probability problems (dice, cards, weather, etc). Blitzstein and Hwang have R code and an online companion website, Grimmett and Welsh do not. Blitzstein and Hwang have about 600 exercises, Grimmett and Welsh have about 400. Blitzstein and Hwang is close to 600 pages, Grimmett and Welsh is 270.

What it comes down to, in my opinion, is that Blitzstein and Hwang is an excellent book for a wide variety of audiences trying to learn probability. Grimmett and Welsh are clearly focusing on math students — it is narrower, has fewer excursions, and is probably more difficult as a text. The material appears simple until you try to do the exercises, at which point you realize that there were many ideas contained in a few words. When you complete the exercises, you feel that you have learned something, and it stays with you. At least, those are my fond memories from twenty-five years or so ago. I have no reason to doubt that the results of working through the current edition will last a similarly long time.

Peter Rabinovitch is a Senior Performance Engineer at Akamai, and as been doing data science since long before “data science” was a thing.

1. Events and probabilities
2. Discrete random variables
3. Multivariate discrete distributions and independence
4. Probability generating functions
5. Distribution functions and density functions
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