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The probability class I recently finished (taught at an upper-undergraduate or lower-graduate level) used the text by Grimmett and Stirzaker. I really disliked this book.

I am familiar with measure theory, so it is fine if the book is measure-theoretic. However, I want to make sure the book doesn't neglect to provide a clear explanation of a the basic concepts of probability, and provide exercises for the basic problem-solving techniques. Also, I always love texts that have good motivation and intuitive explanations for things (I guess I prefer some motivating discussion rather than a totally formal text like Rudin, or arguably Ahlfors).

I think model texts for what I'm looking for are Spivak's Calculus and Dummit and Foote's Algebra. What I love about these texts are the large amount of (enlightening) exercises.

Update: Still looking for a good probability text. Feller's text has come up as a suggestion. Does that one have good exercises?

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    $\begingroup$ What is ISO Probability? How does that relate to ANSI Probability and IEEE Probability? $\endgroup$ – dfeuer Dec 19 '13 at 17:31
  • $\begingroup$ @dfeuer It's a standard internet abbreviation meaning "In search of". :) $\endgroup$ – Eric Auld Dec 19 '13 at 17:31
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    $\begingroup$ Regarding bullet point 2, and a propos of nothing, I have found my left hand pantomiming "Ctrl+F" on the textbook itself when encountering that exact problem.$${}{}{}$$It never works, in case you're curious. $\endgroup$ – Emily Dec 19 '13 at 18:03
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    $\begingroup$ I've heard that William Feller's An Introduction to Probability Theory and its Applications, a text that spans two volumes, is outstandingly good. Full disclosure: I haven't read the book I recommended. $\endgroup$ – Newb Dec 19 '13 at 23:30
  • $\begingroup$ I don't know if you can find this anymore. But An Outline of Statistical Theory by Goon, Gupta & Dasgupta is a great exposition of measure-theoretic probability. Comes in two volumes. The first one is yours. The second is about inferential statistics. $\endgroup$ – Ishfaaq Mar 15 '14 at 7:14
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[1] Capinski and Kopp (1998): "Measure, Integral and Probability". Springer, NY. [2] Bertsekas and Tstsiklis (2002): "Introduction to Probability". Athena Scientific.

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  • $\begingroup$ Thanks for the advice! These seem to have few exercises, so I'm still looking. $\endgroup$ – Eric Auld Mar 15 '14 at 7:53
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I would recommend Sheldon Ross's "Introduction to probability Models" and George Casella& Roger Berger's "Statistical Inference". Ross's book includes probability and stochastic process. Casella's book includes probability and basic statistics. One common thing is they both have clear and intuitive explanations and large amounts of examples and exercises, and exercise solutions are available online.

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Feller's book has two volumes, the first one is the treatment of discrete probability, and the second one is a measure theoretic approach. The first volume is wonderful for a first thoughtful encounter with a probability theory, with tons of motivation, historical remarks, and some good exercises, and I do not have a definite opinion on the second volume.

It is not clear what kind of textbook you are looking for. Grimmett and Stirzaker show tons of techniques to tackle particular (very often than not applied) problems. They do not spend too much time on the foundations. So if your focus is more application oriented, I would say: Get first volume of Feller and enjoy.

However, if you are looking for a rigorous measure theoretic introduction to probability, you should try something else, and I would not recommend to start with second book by Feller. The choice is very wide here, and here are two my favorites (although they change very often):

The first one is very detailed introduction to theoretical probability theory (together with a short but nice exposition of "elementary" discrete probability), you may find it too dry.

The second is a recent textbook with a very thoughtful exposition. The choice here is completely personal.

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  • $\begingroup$ The text by Shiryaev looks awesome! Just what I am looking for. Thanks for the great answer. $\endgroup$ – Eric Auld Mar 21 '14 at 19:19
  • $\begingroup$ @EricAuld You're welcome. $\endgroup$ – Artem Mar 21 '14 at 19:29
  • $\begingroup$ I have bought Feller and Shiryaev. Have looked at Feller so far. One disappointment about Feller is that volume 1 totally eschews continuous sample spaces. These seem important. (I guess I really like the choice of topics in Grimmett and Stirzaker; I just cannot stand the formatting of the book.) $\endgroup$ – Eric Auld Apr 14 '14 at 4:14

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