I don't use any probability theory in my day-to-day work; I've taken a graduate-level probability course, where the lectures, homeworks, and exams were all proof-based material. I've also taken an undergrad course in probability, which was more applied and computational.
I would like to revisit probability theory, as a hobby. My question is:
What are the benefits of studying this subject theoretically, e.g. studying the limit theorems that would require knowledge of measure-theoretic analysis? I don't see how studying probability in this abstract manner, e.g. seeing and understanding the proofs, is beneficial.
Also, can you recommend a good reference that might do a good job at both the theoretical and computational aspects? I know for computational, there's the book by Sheldon Ross, but I'm not aware of a classical theoretical book that's widely respected and used.
Maybe there's a classical paper to read?
Thanks,
Best Answer
The main point of a more theoretical approach are not the proofs, but the greatly enlarged zoo of concepts, paradigms, and theorems. To do urn and similar problems you can stay with the undergraduate probability course. But when it comes to more difficult questions, like "How many bits of information are in a letter $m$ in the English language?", "When shall I stop interviewing a chain of $20$ applicants for a job, and take the present one?", "What is the expected length of the longest run in a random binary string of length $10\,000$?", etcetera, then you cannot do without a fullfledged probability theory course.