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Has anyone compiled a moderately comprehensive list on the web or elsewhere of textbooks on probability

  • For students who have not been introduced to the subject before

  • That introduce both discrete and continuous probability distributions and their cumulative distribution functions, and include things like the Poisson limit theorem, the central limit theorem (say the former with proof and the latter not necessarily), and

  • That perhaps cover the simplest stochastic processes like the Poisson process or infinite sequences of Bernoulli trials?

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I would avoid Feller, vol. 2:) On the other hand, I remember reading Uspensky's (1935?) book with enjoyment. Its proof of the central limit theorem with everything explicit was (to me) wondrously complicated. –  marty cohen Dec 11 '11 at 6:10
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My guess as to the answer to your question is "no, at present", but I suspect the comments on this question will eventually change the answer to "yes", with the answer being a link to your own question. My addition to the list is Peter Whittle's "Probability via Expectation"--- although I do not have it handy, if memory serves, it satisfies all of your requirements. –  leslie townes Dec 11 '11 at 8:56
    
This seems like an extremely specific list that you're looking for. –  Graphth Dec 12 '11 at 2:18
    
David Stirzaker - Elementary Probability could be what you're looking for... –  ae0709 Dec 26 '11 at 1:57
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Measure, Integral and Probability by Capinkski and Kopp is a good book. –  Shahab Sep 24 '12 at 17:03
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4 Answers

I'm just finishing and undergrad course in Probability Theory using A First Course in Probabilty by Ross (8th Ed). it covers pretty much every topic on your list, starting with basic combinatorial principles and the basic axioms of probability and building from there. It covers all the major discrete & continuous distributions, with density, cumulative density, and moment generating functions.

The material is generally well presented, rather reliant on examples though. If you're looking for a textbook to teach/learn from, it's excellent. If you're looking for reference material, I'd keep looking for something more compact.

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I agree. That book has a lot of classic examples. –  geraldgreen Dec 15 '11 at 21:22
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I am nearly finished teaching a course from Jim Pitman's book Probability; it fits this description. I think it's a good book -- it's reasonably easy to read, and has a very large number of exercises. I think having many exercises is especially important for a first probability course because especially at this level, probability is more oriented towards problem-solving than theory-building, and the only way to get practice with problem solving is to solve problems.

Two disclaimers are in order: (1) it's the book I originally learned this material from, so I may have a certain irrational fondness for it; (2) I know Jim Pitman.

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Hello, Michael, you have been a wonderful stat instructor. Thanks a lot for a great semester. But I think the textbook we used is a little bit outdated in terms of visualization. –  geraldgreen Dec 15 '11 at 21:16
    
I agree! If I teach this course again I will keep that in mind. –  Michael Lugo Dec 16 '11 at 0:31
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I first learned probability from the great 1971 classic, Introduction To Probability Theory by Hoel, Port and Stone and the very sure hand of Professor Stefan Ralescu at Queens College. Even with the ton of probability textbooks out there now, I still think there is no better textbook for the rigorous undergraduate math major with a good calculus background. I also found the book by DeGroot and Schervish's very readable and complete, particularly for mathematical statistics. Those are my recommendations-but be leery. More then half the introductory probability textbooks today aren't worth the paper they're printed on and most of them are ridiculously expensive.

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Schervish. ${}$ –  cardinal Dec 11 '11 at 22:16
    
@cardinal My bad,my apologies.Fixed it. –  Mathemagician1234 Dec 11 '11 at 22:28
    
I like de Groot & Schervish. –  Michael Hardy Dec 12 '11 at 18:30
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Here are the items listed here so far:

  • I remember reading Uspensky's (1935?) book with enjoyment. Its proof of the central limit theorem with everything explicit was (to me) wondrously complicated. – marty cohen
  • My addition to the list is Peter Whittle's "Probability via Expectation"--- although I do not have it handy, if memory serves, it satisfies all of your requirements. – leslie townes
  • David Stirzaker - Elementary Probability could be what you're looking for... – ae0709
  • You might like to post this query on allstat, which is a very responsive email list (mainly UK-based). – user42520

    [A comment rather than an answer. But I haven't done this yet and maybe I will.]

  • Measure, Integral and Probability by Capinkski and Kopp is a good book. – Shahab

  • I'm just finishing and undergrad course in Probability Theory using A First Course in Probabilty by Ross (8th Ed). it covers pretty much every topic on your list, starting with basic combinatorial principles and the basic axioms of probability and building from there. It covers all the major discrete & continuous distributions, with density, cumulative density, and moment generating functions.

    The material is generally well presented, rather reliant on examples though. If you're looking for a textbook to teach/learn from, it's excellent. If you're looking for reference material, I'd keep looking for something more compact.

    Drew Christianson

  • I am nearly finished teaching a course from Jim Pitman's book Probability; it fits this description. I think it's a good book -- it's reasonably easy to read, and has a very large number of exercises. I think having many exercises is especially important for a first probability course because especially at this level, probability is more oriented towards problem-solving than theory-building, and the only way to get practice with problem solving is to solve problems.

    Two disclaimers are in order: (1) it's the book I originally learned this material from, so I may have a certain irrational fondness for it; (2) I know Jim Pitman.

    Michael Lugo

  • I first learned probability from the great 1971 classic, Introduction To Probability Theory by Hoel, Port and Stone and the very sure hand of Professor Stefan Ralescu at Queens College. Even with the ton of probability textbooks out there now, I still think there is no better textbook for the rigorous undergraduate math major with a good calculus background. I also found the book by DeGroot and Schervish's very readable and complete, particularly for mathematical statistics. Those are my recommendations-but be leery. More then half the introductory probability textbooks today aren't worth the paper they're printed on and most of them are ridiculously expensive.

    Mathemagician1234

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