This notation doesn't require graduate-level statistics knowledge, it's more like stuff that would be covered in a first mathematical course on probability and statistics. It's totally practical to learn this stuff on your own from videos, books, and PDFs. First you need to get a solid conceptual grasp on probability distributions and their associated concepts like random variables, conditional probability, and joint probability. Then you'll be ready to learn some mathematical statistics and follow along with all the notation.

Note that you don't need to go deep into measure-theoretic probability or any of that stuff that requires more advanced prior education in math.