What are some good books on the theory of probability?

Question

I am planning to study theory of probability. I studied it when i was in high school. I was trying to solve a problem and i felt that i have forgotten most of it. Can anyone suggest any an easy to read book on it.

Answer 1

Try to take a look to MIT OpenCourseWare course material. If you want a proper book I can't help.

Answer 2

I recommend a wonderful book by Robert Trueblood and John Lovett called "Data Mining and Statistical Analysis Using SQL." Not only do they give a pretty good overview of commonly used statistical methods but they show you how to implement actual T-SQL code to make it useful in software.

Every other stats book I've read simply doesn't take the information and make it "live" for software developers.

Answer 3

hi, you might want to look at this previous discussion too:

statistics-book-recomendations

and this one too, although it covers more than just probability:

mathematics-for-computer-science-students

Answer 4

If you're coming back to the subject after a long time, you might get a lot out of Head First Statistics. There are only a couple of chapters that deal specifically with probability, but that will be the case with almost any statistics book.

Answer 5

A short, simple and readable book:

• Probability theory: a concise course by Y. Rozanov

A not-so-short, not-so-simple, but a true classic indeed, is

• An introduction to probability theory and its applications, volume 1 by W. Feller

Answer 6

You might enjoy the cartoon guide to statistics as a friendly introduction. I also find these review notes rather nice.

Answer 7

Probability and Random Processes by Grimmett and Stirzaker is a classic & quite comprehensive.

Not exactly light reading, however....

Answer 8

If you want a good introduction that starts pretty much at the begining and includes plenty of worked examples, I'd recomend A First Course in Probability by Sheldon Ross. Virtually any probablity problem you'll face while doing 'normal' programming will be covered in this text.

Grimmett and Stirzaker, as already recommened is also a great book, but definitly on a more advanced level than Ross. If you get through Ross and want to learn more, Grimmett is a good second book. Probability: Theory and Examples by Durrett would also make a good second book.

But be aware that most of the material covered in these books are of a more advanced and theoretical level than you're likely to need for most programming tasks. If you don't have at least a couple of years of solid university level math under your belt many of the concepts covered in these books may be hard to grasp.

Another a book I quite like is Probability, Statistics, and Stochastic Processes by Peter Olofsson. As the name suggestes it covers more than just probability theory. While it may not cover quite as much probability as Ross, it covers all the important things, plus gives you a bunch of info on two other important and related topics 'for free'.

But for easy to read and covering the basics, go for either Olofsson or Ross. Ross has more worked examples, Olofsson will also introduce you to statistics and stochastic processes, and either will probably suit your needs.

Answer 9

Classical probability books rarely deal with algorithms and applications to computer science and programming. I can recommend Probability and Computing as a starter. Definitely more accessible than Randomized Algorithms (a classic) and gets to interesting applications quickly. Both of these books provide an overview of probability that is enough to get started working on problems.

Answer 10

John, I will stick to your question, which is not to study Statistics (which you know well) or Probability and Computing and whatnot, but Theory of Probability, by which I mean measure-theory-level Probability. The best modern (no Feller or even Breiman, please) textbook is still, in my opinion, Billingsley's "Probability and Measure" (3rd ed.). The only problem with this book is that it does not cover martingales well. I recommend enthusiastically William's "Probability with martingales", which is svelte, selective (no ergodic theory), but a great book.

The official book at Stanford for the grad probability sequence was Durrett's "Probability: theory and examples" (3rd ed.) That's an acquired taste for me, but it's complete.

When I need a reference or just suffer, I use Kallenberg's "Modern Probability".