Good free online PDFs for probability and statistics (with practice problems and answers)? I'd like to rebuild from the ground up and really make sure I have a strong grasp on probability and statistics.
I am able to compute answers in a pinch but I'd like a more formal understanding so I can really ensure I am being systematic about it. For example I have no idea what a probability mass/density function is.
Are there any good resources that go over all the basics and fundamentals while also providing answers to check my work against?
 A: A warm suggestion: Go online to half.com or amazon and look for a used statistics book. You don't need the latest version (expensive), you can also go for a previous version (=cheap, I would have given you mine for free if you had lived around the corner). My favorite: Introduction to statistics by Mario Triola, from which I taught the course couple of semesters to nursing students. I liked the book, good explanations and examples. (But there are other stats books as well).  The answers (odds) are in the back, stats tables are with it too, and if not, those are available on the internet as well. You got everything in one book instead of bunch of PDF's. And if you get stuck on a problem, post it on MSE and we can help...Good luck!
A: Are you interested in understanding probability theory/statistics or just using probability theory/statistics? You say "build from the ground up" and to me that means diving straight into measure theory. On the other hand, you might have never even taken a calculus class, which will make understanding what a probability density function is very difficult as, given a random variable $X:\Omega \to \mathbb{R}$ it is defined as the Radon-Nikodym derivative of a probability distribution (an induced measure) $\mathbb{P}(X^{-1}(\omega))$ with respect to $\mu$, the Lebesgue measure on $\mathcal{B}(\mathbb{R})$. For basic statistics, this is unnecessary but for a deeper understanding and for some applications, it is VERY necessary. Can you elaborate on your background/goals?
