I am taking a probability and statistics course soon and would like to find a text book that is targeted more towards math majors rather than engineers (which is what this class is).

The book my class will officially be using is Probability and Statistics for Engineering and the Sciences by Devore (ISBN-13: 978-0538733526). To be clear I have not seen the book yet but for now I am assuming it is not what I am looking for.

To give an idea of mathematical maturity and (possibly) relevant background by the time I plan to really start looking through whatever book I end up getting I will be through the integration chapter of Rudin's Principles (ch6), be through a course of point set topology (Topology and Groupoids), and I have familiarity with Linear Algebra (I have been learning from Course of linear algebra and multidimensional geometry by Ruslan Sharipov and getting exercises from various books).

I don't have any real specification other than it doesn't focus on ad-hoc calculation skills and has a good amount of theory. Also the book should be a first course book, so it shouldn't assume previous probably and statistics classes. Also the book could be probability or statistics(not necessarily both). Here are some things that would be nice to have but not necessary: a book that covers a lot of the material from the book that will be used in the class; a book that has special topics or applications to things like number theory or combinatorics (basically anything separate from probability and statistics); not greater than 500 pages; reasonably priced.

There are already many questions that have asked for probability or statistics books, but it is not obvious from the questions and answers (that I have seen) that any of those books fit what I am looking for. It looks like this answer might have what I am looking for but it is hard to tell and its expensive.

Edit: What am looking for is not necessarily a replacement for this class, I just figure that I might as well learn some probability or statistics at a more sophisticated level while I am taking the required class that I suspect is more focused on calculations.

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    $\begingroup$ Though it doesn't contain applications, I like Sheldon Ross' A First Course in Probability. $\endgroup$ – David Mitra Aug 15 '13 at 15:46
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    $\begingroup$ North American books with titles that include both probability and statistics are designed for a particular kind of course. They can be good, but are not designed for somebody with your background. $\endgroup$ – André Nicolas Aug 15 '13 at 15:51
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    $\begingroup$ @AndréNicolas I figured that is the case. I guess I should put a little more emphasis that the text book I am looking for is not necessarily a replacement for this class, I just figure that I mine as well actually learn some probability or statistics while I am taking the required class. $\endgroup$ – user29123 Aug 15 '13 at 16:01
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    $\begingroup$ The Devore book has been around a long time, I used it quite a number of years ago. It is good of its kind, $\endgroup$ – André Nicolas Aug 15 '13 at 16:08
  • $\begingroup$ Does this answer your question? Recommend a statistics fundamentals book $\endgroup$ – Intellectually disabled Dec 23 '20 at 3:04

I have answered some similar questions earlier, so give references for those. Se my answer to https://stats.stackexchange.com/questions/63760/inference-for-the-skeptical-but-not-math-averse-reader/63820#63820 but maybe my answer to this one https://stats.stackexchange.com/questions/38082/frequentist-statistics-references-for-someone-well-versed-in-modern-probability/38084#38084 is even more relevant!


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