I am looking for a reference to learn probability theory which satisfies the following criteria:
- Not beginner oriented, but starting from the basis. That means, it can assume the reader to have some mathematical maturity, and analysis, linear algebra, etc can be assumed from page one. On the other hand, it should assume no knowledge of probability itself.
- Concise but still showing some examples. I would prefer something rather brief, say within 300 pages, if shorter and still understandable better. A subset of a longer book is of course also fine. It should cover the basic results of probability one should know (if I knew what it should include I would not need such a book, but imagine central limit, Bayes theorem and other such things should be there).
- It should not be sloppy, but I am mostly interested in learning how to use probability to solve problems rather than in the discipline per se, so I am not looking for a totally abstract text in measure theory or similar things.
Why am I looking for this: I would like to get a first understanding of machine learning and other data science techniques. I do not want to rush copy-pasting code and applying recipes without any understanding of them, so I am trying to get some grounding in probability and statistics, two subjects I know exceedingly little about. On the other hand, I am not trying to prepare to do research, and it should not take exceedingly long (4-6 weeks is roughly the amount of time I am planning to spend on this).
I hope that there is something satisfying these criteria around there!
EDIT: I have opened a similar question asking for references in statistics here.