I never had the  opportunity to visit a stats course from a math faculty. I am looking for a probability theory and statistics book that is complete and self-sufficient. By complete I mean that it contains all the proofs and not just states results. By self-sufficient I mean that I am not required to read another book to be able to understand the book. Of course it can require college level (math student) calculus and linear algebra.

I have looked at multiple books and I didn't like any of them.


DeGroot & Schervish (2011) Probability and Statistics (4th Edition) Pearson

This is not complete enough. It just states a lot of stuff without the derivation.  Besides that I like it.
Wasserman (2004) All of Statistics: A Concise Course in Statistical Inference Springer.

Didn't like it at all. Almost no explanations.


"Weighing the Odds" from David Williams is more formal than DeGroot and seems to be complete and self-sufficient. However, I find the style strange. He also invents new terms that only he seems to use. All the stuff that is explained in DeGroot too is explained better there.

If you know a great book in German that's also fine as I am German.

If you are searching for proofs, I have been working for some time on a free stats textbook that collects lots of proofs of elementary and less elementary facts that are difficult to find in probability and statistics books (because they are scattered here and there). You can have a look at it at http://www.statlect.com/