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Question is quite straight... I'm not very good in this subject but need to understand at a good level.

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what do you mean by probability and to what level do you need it? –  picakhu Apr 9 '11 at 3:06
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I meant a statistics subject and I want a level that make easier to do exams. The books I have always gaps on explanations and that's make me crazy... –  Eduardo Xavier Apr 9 '11 at 3:23
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@Eduardo: it is hard to say what will work for each individual, but for an admission exam, probably previous test papers will be most useful. –  picakhu Apr 9 '11 at 5:15
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As noted, there are different sorts of "probability". (1) a branch of finite combinatorics (2) assuming knowledge of Riemann integral (maybe even Riemann-Stieltjes integral) (3) presupposing measure theory. Answerers should explain which of these they are talking about. –  GEdgar Apr 9 '11 at 14:10
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@GEdgar: yes, but even more the questioner should make more precise what he is looking for. It is very inefficient and a waste of people's time to ask for a spray of all possible answers. In fact I think this is as yet not a real question and I am voting to close... –  Pete L. Clark Apr 11 '11 at 6:02

7 Answers 7

up vote 19 down vote accepted

For probability theory as probability theory (rather than normed measure theory ala Kolmogorov) I'm quite partial to Jaynes's Probability Theory: The Logic of Science. It's fantastic at building intuition behind the rules and operations. That said, this has the downside of creating fanatics who think they know all there is to know about probability theory.

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If anybody asks for a recommendation for an introductory probability book, then my suggestion would be the book by Henk Tijms, Understanding Probability, second edition, Cambridge University Press, 2007. This book first explains the basic ideas and concepts of probability through the use of motivating real-world examples before presenting the theory in a very clear way. I found a nice feature of the book the fact that simulation is deliberately used to develop probabilistic intuition. The book also discusses more advanced topics you will not easily find in other introductory probability books. The more advanced topics include Kelly betting, random walks, and Brownian motion, Benford's law, and absorbing Markov chains for success runs. Another asset of the book is a great introduction to Bayesian inference.

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An Introduction to Probability and Random Processes by Kenneth Baclawski and Gian-Carlo Rota is very good, though it does require the reader to have or develop mathematical maturity.

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Here is a list of great books to own to learn probability & statistics. Some on the list like programming in R are great add-on stuff to know.

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I wouldn't know which book is the best, because I've only used two when I was taking a course in probability, but if you'd prefer videos , I'd suggest:

MIT 6.041SC Probabilistic Systems Analysis and Applied Probability course , which is available in MIT OpenCoursWare for free :

https://www.youtube.com/playlist?list=PLUl4u3cNGP60A3XMwZ5sep719_nh95qOe

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While not a book, Sal Khan's site: http://www.khanacademy.org/ offers dozens of short videos that provide introductions to probability and statistics. Many of the videos even have problem sets associated with them. Khan provides accessible and often intuitive explanations.

He also has extensive video lessons on algebra, linear algebra, calculus, and geometry as well as physics.

All for free.

Find a discussion on this forum which explores pro's and con's about Khan at:

What does Khan Academy have to offer? Depth? Rigor?

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