Recommendation on probability and statistic books.

Question

I'm currently starting to self study probability and statistic, a friend recommend me to use a book he has but his book does not go deep in the theorem and formula, instead it just state the equation and when to use it along with some properties but not the proof for the equation (for example: the chapter about the Poisson random variable just tells you how to use it and when, but lacks the proof of how mathematicians arrive at that complex equation ). I would like a book that is rigorous and proof-based for every problem in it ( like Tom M. Apostol's calculus books for example), im a colleague student and has good calculus and linear algebra background so an more advance than regular books is ok with me. Do you have any recommendation ?