Secondly, pour a pot of cold water here (it doesn't matter if you don't understand it for a while, just have a general direction): there is no shortcut to learning dry goods. To really study mathematical statistics systematically and thoroughly, you need calculus, linear algebra and probability theory (especially probability theory! ) basic knowledge. Calculus is the basic tool of advanced calculation; Linear algebra is to simplify the relationship between variables and facilitate subsequent understanding and calculation;
Probability theory is the basis and source of the branch of mathematical statistics. Many basic concepts about data and almost all theorems related to statistics in advanced mathematics are explained in probability theory, such as variance (D[X]), expectation (E[X]), common data distribution, central limit theorem (CLT) and strong/weak law of large numbers. ...
Why: You may think that what you want to learn looks much better, and the theorem mentioned later is a bit vague, so it is normal that you can't understand it for a while. I'll try to spoil it here, so that you can have a certain understanding of the importance and practicability of probability theory. Theoretically, all types of data can tend to the same distribution through proper processing, that is, the standard normal distribution N(0, 1), if the data is large enough and has no obvious distribution characteristics (in reality, this situation is much more standardized than in books)! If you just want to know mathematical statistics because of the need of non-scientific research and your work is not rigorous, or you really don't want to spend too much time on advanced mathematics, then I suggest you simplify the study of calculus and linear algebra and focus on: necessary concepts and theorems (just know what it is, don't need to know why); Data processing software, such as R, S, etc.
Above. Good luck with your studies.