There's a middle path between rote memorization of outcomes, and building everything up from first principles. And I'm guessing it's probably what the parent poster had in mind.
A great statistics textbook along these lines is Principles of Statistics by MG Bulmer. It's one of those Dover classic textbooks that you can get for cheap. This book assumes you already know basic calculus and combinatorics. It then goes through a series of practical problems, and shows how you can use calculus or combinatorics to solve them. And, along the way, an intuitive and holistic perspective on statistics begins to form.
The overall effect is great. It's a lot like a 3blue1brown video series, only from the 1960s, and with problem sets.
A great statistics textbook along these lines is Principles of Statistics by MG Bulmer. It's one of those Dover classic textbooks that you can get for cheap. This book assumes you already know basic calculus and combinatorics. It then goes through a series of practical problems, and shows how you can use calculus or combinatorics to solve them. And, along the way, an intuitive and holistic perspective on statistics begins to form.
The overall effect is great. It's a lot like a 3blue1brown video series, only from the 1960s, and with problem sets.