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To give you some background, I have a grasp on the basics of statistics and probability theory and even remember touching Bayes theorem at the university data mining course. But being a few years away from the university made my math got extremely rusty (so much for last-minute pre-exam cramming). While I remember various random basic concepts, there are a lot of gaps in my understanding of them.

What would be a good material (a book, a site, or otherwise equally accessible medium) to revise the fundamentals and go beyond basics? I'd like a book that can be actually read as a book (most statistics books are really dry and are close to being reference material, rather than a book).

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  • $\begingroup$ You may want to ask this at stats.stackexchange.com $\endgroup$ – Jyotirmoy Bhattacharya Oct 7 '10 at 5:54
  • $\begingroup$ @Jyotirmoy Thanks for the pointer, I've completely missed this one. Probably someone with enough rep should migrate this question, I'd like to avoid cross-posting. $\endgroup$ – Alex B Oct 7 '10 at 5:57
  • $\begingroup$ Yes, there's a parallel thread on the stats site. But this one focuses on readable texts that would be of interest to mathematicians, so I think it merits staying in its current location. $\endgroup$ – whuber Oct 7 '10 at 21:12
  • $\begingroup$ If you just want a review, just read Schaum's Outline of Probability and Statistics. It's less than $16 new. $\endgroup$ – Apprentice Queue Mar 16 '11 at 22:17
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Freedman, Pisani and Purves, Statistics, followed by Freedman, Statistical Models.

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    $\begingroup$ I'm going to answer only as a comment here because IMHO this is the best answer going and I'd love to see it voted up as much as possible. But Huff's "How to Lie With Statistics" and Gonick & Woolcott's "Cartoon Guide to Statistics" deserve consideration as supplemental reading! $\endgroup$ – whuber Oct 7 '10 at 21:11
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    $\begingroup$ FPP is definitely readable. (Incidentally, I'm currently teaching a course from it.) But it might be a bit low-level for this particular person. $\endgroup$ – Michael Lugo Oct 8 '10 at 4:36
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Alex i recommend you these two books:

  • Introduction to Probability by Sheldon Ross

  • An Introduction to Probability Theory and Its Applications: William Feller

Both are very good books for an introductory level and the second one is a classic. It's referred by many people.

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Many people recommend the book All of Statistics: A Concise Course in Statistical Inference by Wasserman.

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Here is good collection of books for statistics and probability. But the point you make is a valid one. To maintain interest you really don't want a "dry" book, but something that gets into just enough excited to pursue the subject more. hth.

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Here is one that is used to get future and present students of financial engineering up to statistical speed: R. Dimitric: Mathematics for Financial Engineering. Can find it for instance on Amazon

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For an interesting book, why not try 50 challenging problems in probability by Mosteller? That might be the book you're looking for. Somebody has already mentioned Feller, but that is too much for bedtime reading.

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