This question follows from my previous question. I want a book that deals probability theory rigorously (and cover as many topics as possible) yet not involving much about measure theory. There are too many books totally geared to students majoring in other fields, so it's a shame that actually for mathematicians it became so hard to find a good book on probability theory(same as in the field of linear algebra).
I got a recommendation of Ash's Basic Probability Theory, which I'm reading a bit. Just wanted to buy a book for me to be well prepared for further learning in this field. I've searched and these books also look pretty decent:
- Introduction to Probability Theory(Paul G. Hoel, Sidney C. Port, Charles J. Stone)
- Probability and Random Processes (Geoffrey R. Grimmett, David R. Stirzaker)
- Elementary Probability(David Stirzaker)
I think the second book also deals with a bit of stochastic probability theory, but anyway I'm currently taking the class (check my previous question up there) and it really deals with a lot of different subjects so I was thinking of buying the book.
My question is: Granted that I've taken basic probability theory before(so I don't need too much easy textbook), what is your best recommended textbook for a rigorous treatment of probability theory yet not involving much about measure theory?
The more subjects it covers, the better as far as this condition is satisfied.
Please remember that I'm not an engineer: my first probability class used the textbook 'A first Course in Probability' by Sheldon Ross, and I hate the book with passion.
Thanks in advance.