Ask HN: Book which comprehensively covers probability theory?

E.T.Jaynes: "Probability Theory, The Logic Of Science"

I recommend "Introduction to Probability" by Joseph K Blitzstein and Jessica Hwang.

This book is tough. Really tough. However, you are really going to do "deliberate practice" while having a go on the assignments.

It bothers me that the author does not provide the answer to most of the questions. This is specially bad in this field of Mathematics (Probability). As an example, in calculus you can always plot the curve, the derivative and see if the result makes sense, in probability theory it is hard to have a simple and safe sanity check.

You can watch all classes from Harvard here for free: https://www.youtube.com/watch?v=KbB0FjPg0mw&list=PL2SOU6wwxB...

If you want, there is also a MOOC in EdX with the same material: https://www.edx.org/course/introduction-to-probability-0

Sheldon Ross' book is also a good one. It was mentioned here. I specially like the section on theoritical problems, only with exercises on proofs. Every chapter has one. However, Joe Blitzstein problems are more challenging and will train you more on intuition.

I recommend the probability chapters of 'Information Theory, Inference, and Learning Algorithms' [1]. I think this book is good because it starts off with balls in hats and goes on all the way to a Bayesian simulation of a Neuron and other subjects relevant for machine learning.

It's available for free online, although most people I know end up buying the book[2].

[1] http://www.inference.org.uk/itila/

[2] http://www.inference.org.uk/itprnn/book.pdf

Ch. 1-5 of Sheldon Ross's "A First Course in Probability" works for this purpose. Consider testing/hardening your knowledge with Mosteller's "Fifty Challenging Problems in Probability".

Feller's two volume classic [1] has plenty of motivation - his exposition of combinatorics at the beginning of the first volume is a great introduction to that subject! However, it wasn't written with algorithms in mind.

Venkatesh's more recent volume [2] is very well motivated and is better suited to modern engineering applications. Both have lots of exercises.

[1] https://www.amazon.com/Introduction-Probability-Theory-Appli...

[2] https://www.amazon.com/Theory-Probability-Explorations-Appli...

https://www.youtube.com/playlist?list=PLm3J0oaFux3aafQm568bl... Some lectures on basic probability combined with some rigorous notes specific to CS http://www.cs.cmu.edu/~odonnell/papers/probability-and-compu...

I've been working through "Probability - For the Enthusiastic Beginner" by David Morin. Very affordable for a textbook, clear instructions, solutions to exercises in the book is provided.