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Looking for a textbook for a two-semester course in probability and (theoretical) statistics

Dikran Karagueuzian writes:

I am in the process of choosing a textbook for a junior- or senior-level undergraduate two-semester sequence in probability and statistics.

I would be obliged if you could recommend one which is free (or at least cheap), or inquire with your blog readers for such a recommendation.

The course has been taught successfully in the past using Mathematical Statistics with Applications, by Wackerly, Mendenhall, and Scheaffer. Also at roughly the right level is Probability and Statistics by deGroot and Schervish. However, the current edition of the first text now lists for $217, and I find myself embarrassed to ask students at a public university to pay prices at this level.

The main item on my wish list, other than the textbook being cheap and at the right level, is that it should be possible to teach the course by following the book closely for the entire year. (I have never taught the course before and have spent several years away from the university in the private sector. Thus, 3 weeks from source A, 4 weeks from source B, and 5 weeks from source C is likely to turn out badly.)

I have looked at online statistics resources like without finding a suitable textbook.

Of course, I could choose one of the two texts mentioned above if nothing turns up.

Any help you or your readers could offer would be very much appreciated.

My reply:

Statistics: What’s the Difference isn’t ready yet, and it’s even further from being ready at the mathematical level you’re looking for. I’ve never actually taught the course you’re talking about–I did take such courses in college but I can’t say I was thrilled with the books we used. So I’ll throw this one to the readers. Any suggestions?


  1. db says:

    Assign an older version of the textbook you want to use.

  2. anonymous says:

    this is very good, and very cheap for the 1st part of your course:

  3. I don't have any recommendations for a book on statistics, but Grinstead and Snell offer a free pdf version of their book "Introduction to Probability." I'm an anthropologist, so I'm probably not the right one to judge, but I thought the book was very good. Here's the link:


  4. Student (ha! get it? says:

    A student's perspective:

    I really think Wackerly et al.'s Mathematical Statistics with Applications is a fine text and the international edition is easily available online for about $50-60.

    Students are savvier than you think.

    (And if you're worried about the less sophisticated textbook-hunters among them, you may not be able to have the bookstore order the international edition for you, but there's nothing stopping you from listing its ISBN in the syllabus, or from including a link to or

  5. N says:

    Keep using Wackerly et al but ask students to buy a used, older edition. They can get older editions for less than $20 at Amazon or Abebooks.

  6. Antonio says:

    Just curious: Which book is "Statistics: What's the Difference"? :)

  7. Jonathan says:

    I don't have any personal experience with it, but our university uses Bain and Engelhardt. The list price is about $130, but Amazon has it for $90 new and you can often get it for half that used.

  8. Adam Hyland says:

    Grinstead and Snell is free and Free. You can download it at ( The level of sophistication is appropriate for an upper level undergraduate class and the examples/problems are clever. I have some complaints about the structure of the book, primarily that it follows the "first discrete then continuous" path of most stats books but intersperses bits about the central limit theorem and other asymptotic ideas. this tends to make the difficulty curve a bit uneven.

  9. MyOpinion says:

    Casella & Berger seems to be classic here. Used it both in undergrad and grad school. Amazon lists it for $140, but really, I find it invaluable.

  10. Bob Carpenter says:

    What do the students need or want to get out of the class? Personally, I'd want to get an intro to probability theory, modeling and computation. I don't know of one good book to cover everything.

    1) Probability Theory
    I like Ash's basic probability theory book. It's inexpensive. It covers pretty much all the theory you'd need in a one year class and is a bit more rigorous than something like DeGroot and Schervish without being too formal. I don't like the comprehensive probability and stats books as much because they're not quite as precise in defining random variables (not that Ash gets into the guts of Lebesgue-Stieltjes integration).

    2) Modeling
    This is trickier. I really like Gelman and Hill's regression book, which covers both linear regression and GLMs with both point estimation and Bayesian posteriors. It's relatively inexpensive. But you may want something that covers a broader range of distributions in a more general context. Many people have recommended Freedman, Pisani and Purves to me, but it's expensive, and like Gelman and Hill, there may not be enough emphasis on the math side of things. On the other side, Gelman et al.'s Bayesian Data Analysis is probably too much math for a first stab at modeling.

    3) Computation
    You could go with something like the online manual for R. I can't imagine trying to learn stats without a tool like R at hand. Coupled with something like JAGS if you want to cover Bayesian modeling and inference.

    PS: Small world — unless there are a whole bunch of Dikran Karagueuzian's out there, I knew your dad from Stanford. If I recall correctly, you were an undergrad then and used to hang out studying math at CSLI.

  11. Dougal says:

    John Rice's Mathematical Statistics and Data Analysis is what we used in my (semester-long, but we didn't cover the whole book) roughly equivalent class. It's alright.

    For the probability stuff, if you want to focus on probability itself, Grinstead and Snell is good and available as a PDF for free.

  12. Jyotirmoy Bhattachar says:

    Hogg and Craig's Introduction to Mathematical Statistics is $70. A classic, but limited to classical topics. Wasserman's All of Statistics is $66. Has much better coverage though it may need to be supplemented by lecture notes.

  13. Alex Blocker says:

    I'm TFing a course at roughly that level with DeGroot & Schervish at the moment. It's fairly good and has a nice Bayesian focus, but it also organizes some of the core classical inference material somewhat oddly. Also, the problems in the book are far too easy (close to book examples) to make useful homeworks.

    I have a soft spot for Casella & Berger (original training), but it's not quite at the right level for such a course. For the probability theory portion, I'm not sure what your best option is, but, for the statistics portion, Rice's textbook might be a good option. I have seen it used well and like its general organization.

  14. Haathi says:

    Bob referred to Ash's probability text, which is of course excellent and just a touch above the math level of the books mentioned in the message. Ash also has a mathematical statistics text and both this and the probability book is available for free download from Ash's website. I believe Ash's probability text is also available as an inexpensive Dover edition. Hope this helps.

  15. sean says:

    I like the Freedman, Pisani and Purves book that Bob mentioned. It has the additional advantage that it hasn't changed much since the first edition in the 1970s, so your students can buy cheap used copies even if the new one is expensive.

    This is, perhaps, the key to solving your problem–look for books which have been stable enough over time that you can safely recommend that your students buy old editions from Amazon.

  16. Charlie Saunders says:

    At FSU Ross is used in intro to probability and Rice for Math Stats – both 2 semester courses. I don't find either particularly exciting. If you want them to learn theory, Ash's book is good and there is always Cassella and Berger. If they are to do a lot of problems or have applied exams perhaps you can also use one of the Schaum books. Regardless, using R is essential.

  17. doug says:

    Another good text at this level is Evans and Rosenthal's Probability & Statistics: The Science of Uncertainty. Nice mix of modern topics and computation, but, as is typical of these, not much on data analysis. I just checked the price (list $123, but $94 at Amazon), which I guess is not outrageous by these standards.

  18. Former student says:

    My all-time favourite statistics book from my university days is 'An Introduction to Mathematical Statistics and its Applications', by Larsen and Marx.

    The text is clear, the examples use interesting real-life problems and are easy to follow, there's lots of motivation (why are we doing this?) stuff, and even little biographical sketches of historically important statisticians.

    Definitely check it out – your students will love it.

  19. Thomas says:

    A fellow graduate student and I were just chatting today about our undergrad textbooks. We both agreed that Bain and Engelhardt was a great intro text. (Emphasis on the intro. It isn't a rigorous text: I get the sense it is geared toward folks outside of statistics. But, hey, you are teaching an intro class.) Both he and I still go back to it when we've forgotten a formula, etc. The way the book is organized makes it very handy as a reference. (Helpful info on font and back flap.)

  20. Dikran Karagueuzian says:

    Many thanks for the thoughtful suggestions to all who responded.

    There are some institutional restrictions, which perhaps I should have mentioned, so not all the proposals will work. But I am much better off now than I was before, and will spend a few days looking through the texts mentioned here before running a proposal by my colleagues.

    Bob – Yes, you have the right Dikran, and I can be reached by email: dikran at gmail.

  21. What about Wasserman's All of Statistics? My understanding from Larry is that it grew out of precisely such a course, and has certainly been used for one here at CMU for some time. Drawback: the list price is something like $90.

  22. I used Ross for my 300 level probability class, DeGroot and Schervish for my 400 level sequence, WMS when I thought I was going to be an economist, and was subjected to a review of my 400 level sequence, and Casella and Berger in graduate school. I thought Ross was good at discrete distributions, bad at continuous, DeGroot and Schervish was a great all around, WMS was horrible, Casella and Berger is great, but graduate level only (really sparse with the examples and pictures).

    By the way, I never blinked at what I paid for upper division textbooks. Casella and Berger put a lot of effort into Statistical Inference, and deserve to be justly compensated. On the other hand, I do object to what students pay for introductory level texts. I see the barely updated seventh edition of Introduction and Practice of Statistics was just released, with permutated homework numbering and 20% different fluff.

  23. Jerzy says:

    Have you seen Allen Downey's "Think Stats"? It is (1) somewhat of a work in progress, and (2) probably for a different target audience than the math stat book you seem to be looking for… but at least it's a freely available online resource:

    I haven't read it in detail yet, but Downey's earlier book "How To Think Like A Computer Scientist" was quite good.

  24. David Ames says:

    If the professor will acknowledge you, perhaps he will send you the materials indicated in the dead links, and you will have a fair idea what you can do with the deGroot book.