Understanding Probability

by Henk Tijms

Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.

Genres: Mathematics

574 pages, Kindle Edition

First published September 15, 2004

Reviews

[William Schram · Rating 5 out of 5]

With Understanding Probability: Chance Rules in Everyday Life Henk Tijms makes an effort to show that Probability has expanded over the years, from just covering games of chance and their outcomes to being an engineer’s best friend in some cases. Whether it is making a phone network that can handle a full load of calls to engineering a dike that can hold all the rainfall it needs to, probabilities and chance have an important role in our lives.

The book is nice for many other reasons: it is full of examples, the footnotes contain biographical information on certain well-respected mathematicians, it has these little touches that make it charming to read and look at and so on.

The book is divided into 15 chapters. Each chapter goes into a small aspect of probability. From basic rules of chance, all the way up to Markov Chains, it makes me wonder if they have some kind of international standard for textbooks on this subject. In any case, the first six chapters cover Probability in everyday life. Lotteries and gambling and stock investing cover this section. It does certainly make the section interesting. It also covers distributions and statistical applications of probability. The next section covers Probability as well but does so in a deeper and more involved manner. It has a section that involves countable and uncountable sets for instance.

All in all, this was a pretty good text on Probability and was quite enjoyable.

[Flynn Heiss · Rating 3 out of 5]

The first part was a really nice intro to a bunch of probability concepts, completely motivated by A LOT of examples (mostly gambiling). It covered a lot I already knew but also discussed some concepts that I had no/limited knowledge of (Kelly Betting System, random walks, the waiting paradox)

The second half was much more theory and really dry. I still don't really understand moment generating functions; the value seems cool but hard to wrap my head around. Proof of Central Limit Theorem still seems out of reach for me. However, it was good to finally learn what a Markov chain is and how elegant their applications are.

[Hanyu · Rating 5 out of 5]

GOAT

[Rohin M · Rating 2 out of 5]

Read the second half in a day to prep for a machine learning course. I can’t say that I found it particularly helpful but that’s probably my fault more so than the book’s. Still, after browsing through the table of contents I think the first half would be valuable for intuition but the second was just too terse to provide good theoretical foundations. Will have to read Ross’ A First Course in P Theory over the holidays to better understand this stuff.

[Kent Sibilev · Rating 4 out of 5]

A lovely elementary introduction to the probability theory. It is a good supplimentary reading, but it will not replace any decent textbook on the subject. I especially liked the first part of the book, where the basic concepts are introduced.