And actually, it turns out it's about as simple as possible. It's one of those magical things about mathematics. And I'll prove it to you one day. I want to give you a working knowledge first. In statistics, I'm always struggling whether I should be formal and giving you rigorous proofs, but I've kind of come to the conclusion that it's more important to get the working knowledge first in statistics. And then later, once you've gotten all of that down, we can get into the real deep math of it and prove it to you. But I think experimental proofs are kind of all you need for right now, using those simulations to show that they're really true.