# Books for some kind of special self-education in probability and statistics theory?

I am looking for a textbook (or, more likely, a set of textbooks) in English for self-education in probability and mathematical statistics.

I’m a middle-aged person working as data scientist, primarily in market research. I’ve been doing data mining, machine learning, sometimes business modeling, etc. for many years. Now when I have achieved some degree of professional success, I feel that my lack of theoretical education is holding me back from further development.

For example, I can do some relatively sophisticated factor or cluster analysis with Python (mostly using scikit-learn), and I have some basic idea of underlying math behind applied methods, but I’ve never truly understood this math in depth.

Ideally, I’d like to be able to trace the derivation of each statistical test or other application from the very outset—not only in order to comprehend their workings, but to modify them for my situations and to develop plausible derivative applications as well. For example, I’ve written a little module for nominal-ordinal association testing based on some academic papers, but I was only able to convert the described methods into code without real insight into why they work at all. I’d better like to be able to explain every detail of these methods to myself and to any interested person from, say, a high-school level.

I tried to search for the textbooks myself, mostly by investigating search results by Best Textbooks on [Something], but I got completely lost. It is as I should learn some set theory, some combinatorics, some measure theory, some topology, lots of calculus, lots of linear algebra, and probably something else—and this is just to get on with the probability theory. Even if I somehow choose the “best” book on each topic (based on my goals) and get through it, I will be a mess due to huge amount of information and conceptual incompatibility between books (different approaches, scientific communities, explanation methods, notation etc.).

So, I need your advice on what to start with. I’m not afraid of serious and niche literature as long as I can see it can help in my situation; I’m far more afraid of books like σ-Fields Comic Book for Dummies.

• One standard textbook for basic probability theory and elementary math statistics is Wackerly, Mendenhall, Scheaffer. I used several editions of it when I was teaching relevant courses. Requires a full dose of undergrad calculus, but no measure theory. No meaningful use of R. (Mostly correct answers to most odd-numbered problems at the back. More-detailed answers in separate student solutions manuals.) Current edition is expensive, but used copy from several yrs ago just as good for your purposes. Not claiming it is the best, but I can say it's competently written with helpful examples. Aug 23, 2020 at 23:02
• I’m unclear about how the very concept of probability and basic things like convergence in measure can be defined without measure theory. Aug 24, 2020 at 12:53
• Seriously consider starting at the high school level in your reading if you wish to be able to explain methods and principles to high school students. You might then quickly discover that you don't need to venture into measure theory, etc: a little insight and knowledge of the language of statistics can go a very long way.
– whuber
Aug 24, 2020 at 14:39
• Second BruceET's recommendation. I'm working through the 5th Ed. of Wackerly, Mendenhall, and Scheaffer right now. It's quite good. Aug 24, 2020 at 17:15