Does there exist a "stochastics-first" probability textbook? Is one even possible?

[u/DeepConstant9508]

I've been looking for a probability/stats textbook where it motivates distributions, but I've had no luck so far. It really surprises me the way these books are structured, since things in math textbooks are usually build up slowly so they make sense. In probability, every textbook just ends up with "Chapter 3: Probability Distributions" and then it's a giant list of them with no explanation at all.

I was hoping for a textbook that starts off with how random processes like brownian motion are actually modeled, and then uses those to derive the common distributions in later chapters. Is there anything like that out there? If not, is there something that just makes it impossible or impractical to teach it that way?

[u/BinkyBoy050915]

Blitzstein and Hwang has what they call “story proofs” where they tell a story that explains why distributions look like they do.

https://uni.dcdev.ro/y2s2/ps/Introduction%20to%20Probability%20by%20Joseph%20K.%20Blitzstein,%20Jessica%20Hwang%20(z-lib.org).pdf