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I'm looking for a book that provides deep, rigorous coverage of probability theory, but with an emphasis on material that is mostly useful outside of a mathematics department. I've heard "The Theory of Probability: Explorations and Applications" is pretty good, but I wanted to get some other suggestions.

For example, Achim Klenke's book is way too much for me...it's organized for theorem proving, not applications as far as I could tell. Also not a big fan of Durrett's books from what I've perused, or Billingsley or Feller...again, too much of a mathematics research focus.

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1000 Exercices is the best book you can buy. Why ?

  1. Cover the full range of probability.
  2. Provide exercice based of the probability: Put in practise because there is a big gap between Theory books and real Proba problems.

  3. Prepare you well for Quizz, and make your brain in good shape....

  4. You can keep forever as a book of how to solve problems...

http://www.amazon.com/Thousand-Exercises-Probability-Geoffrey-Grimmett/dp/0198572212

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    $\begingroup$ Wow! Impressive coverage! $\endgroup$ – user75138 Mar 31 '16 at 19:22
  • $\begingroup$ Yes, this is focused on how to use Proba rather than how to read the theory... (and never know to use it). $\endgroup$ – quantCode Mar 31 '16 at 19:25
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    $\begingroup$ I think you'd want in addition to this, the actual book: amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/… which has the exact same exercises (but no solutions). I should add that this is one of the few books I've seen which presents advanced probability theory with essentially no measure theory. $\endgroup$ – Alex R. Mar 31 '16 at 19:48
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Frederick Mosteller's Fifty Challenging Problems in Probability sounds made to order for you. Check out the comments on Amazon about it...

http://www.amazon.com/Challenging-Problems-Probability-Solutions-Mathematics/dp/0486653552/ref=sr_1_1?ie=UTF8&qid=1459445736&sr=8-1&keywords=frederick+mosteller

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    $\begingroup$ I think this one does not cover the full range of Probability. This is mainly for brainteaser testing. $\endgroup$ – quantCode Mar 31 '16 at 19:23
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    $\begingroup$ @quantCode How useful is Grimmet's book "outside of a mathematics department?" Mosteller's has two significant advantages: 1) meeting this criterion of being truly applied, and 2) being written by Mosteller, one of the great 20th c statisticians. What it may lack in terms of the "full range" of probability is more than compensated for by it's non-academic focus. $\endgroup$ – Mike Hunter Apr 1 '16 at 19:29
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Applied Probability by Kenneth Lange

  1. Huge breadth of applied probability topics, with a few chapters on computational probability.
  2. Tons of examples (albeit sometimes too concise)
  3. Very good balance between theory and applications.
  4. HUGE collection of good problems, difficulty range from mildly trivial to pretty challenging. I particularly like his problems because most of them are very difficult to do, until you see how to do it and the proof becomes less than 1/3 of a page.

I used this book for a stochastic process class, and it remains one of my all time favorite books.

"Theory divorced from applications runs the risk of alienating many potential practitioners of the art of stochastic modeling. Applications without a clear statement of relevant theory drift in a sea of confusion."

https://www.amazon.com/Applied-Probability-Springer-Texts-Statistics/dp/1441971645/ref=sr_1_1?ie=UTF8&qid=1509045816&sr=8-1&keywords=applied+probability+lange

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