What Are Some Good Resources for Refreshing on Probability and Statistics?

[pergradus]

So my probability and stat knowledge is pathetically weak. I'm a Junior physics/math dual major and I'm going to be taking statistical mechanics and some other higher level physics courses next semester where I would really like to brush up on my probability and statistics.

I really think I need a refresher starting from the ground up - any suggestions on books or good websites for this? I don't need a huge thorough introduction - something more dense and meant for a higher-level reader as opposed to a freshmen or high school student would be better.

Thanks.

 

[micromass]

If you want something meant for a higher-level reader, then I got two books to recommend:

1) "Probability and measure" by Billingsley. This is about the best book on probability theory out there. But it's no book for softies. I suggest skipping the first section, which is kind of confusing.

2) "Statistical Inference" by Casella and Berger. A very good and rigorous stat book.

 

[jasonRF]

A very concise book that I really like is "all of statistics" by Wasserman. From your brief description of what you are looking for it might be the best fit. You can look at sections of it on amazon.

You might want to check out free ebooks as well.

a nice free calculus-based probability book is:
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html

A couple of free books by Ash, one on probability theory (with one chapter on stats), and one on stats, can be found here:
http://www.math.uiuc.edu/~r-ash/
These are at an advanced undergrad level. I don't think they are the easiest reads, but they are reasonably good.

A popular graduate level probability theory book by Durrett can be found at his web site:
http://www.math.duke.edu/~rtd/PTE/pte.html


Even more free books can be found at:
http://www.e-booksdirectory.com/listing.php?category=15
and the "probability" and "statistics" subcategories. You might find what you are looking for there.


My favorite fr/soph level book is "a first course in probability" by Ross. I took a course out of the 3rd edition - which you can find used for cheap! It has no statistics in it, though.

At least in the US, both of the books micromass suggests are usually used in graduate level courses. Billingsly is beyond me, but I really like Casella and Berger - it could certainly be used by an undergrad if they were a little motivated. I have the first edition, and the second edition looks even better (is NOT cheap). A little easier (and old fashioned) probability and statistics book that can also be found much cheaper is "Introduction to Mathematical Statistics" by Hogg and Craig. I picked up a used copy of the 5th edition for a few dollars and I think it is quite good.

Happy reading!

Jason