Calculus based probability books

[sak]

I have seen a lot of discussion about good books for probability, calculus, statistics but was wondering what would be a good book to learn and advance the "Calculus based Probability" skills. I am looking for an intermediate level book.

 

[iddqd]

My favorite probability book is "Probability and Random Processes" by Grimmett and Stirzaker.

Some people consider this book to be "advanced" but I don't think it is that bad if you are comfortable with calculus, mathematical notation, etc. The exercises are non-trivial and they admit as much. I think you can see a pretty good chunk of it on Google Books if you want a preview.

If needed, use the Schaum's outline (Probability, Random Variables, and Random Processes) as a backup as it moves a little slower and works as a good guide to the first 4 chapters or so.

 

[CGiuliano]

I'm currently using "A first course in Probability" -Ross Sheldon. Don't be fooled by the name, this book is definitely at the intermediate level. I would give it a solid 'meh'. The author is a bit frank, and it is is not exactly a fun read. The only upside is that you can google an entire PDF format solutions manual.

 

[sak]

I consider my calculus skills pretty advanced but probability skills to be intermediate. So, in that case where should I start? I checked the books mentioned below but seems like they are are more probability intense and has smaller weight on calculus side. Am I right in my observation?

 

[iddqd]

The Grimmett book starts out using set theory applied to probability but once you get to continuous random variables it's mostly calculus.

If you're concerned about MFE requirements I think they're usually just saying they want your understanding of probability to be beyond the basic combinatorics class they sometimes use as a first class in undergrad. You need to understand random variables and their cumulative distribution, density, and moments. You can't get too far there without calculus.

 

[CGiuliano]

I consider my calculus skills pretty advanced but probability skills to be intermediate. So, in that case where should I start? I checked the books mentioned below but seems like they are are more probability intense and has smaller weight on calculus side. Am I right in my observation?

Calculus, set theory and methods of proving are applied in every chapter. That being said, it is a probability book.

I also, have Schaum's outline (Probability, Random Variables, and Random Processes). I would recommend it as a supplement.

 

[sidd]

I would suggest doing a search before posting.. Had you done that, you would have found some excellent recommendations from ppl like BBW.