Statistics/Probability theory is really deeply tied to calculus/real analysis . Basically any quantity you can think about in statistics or probability is reall

Statistics/Probability theory is really deeply tied to calculus/real analysis . Basically any quantity you can think about in statistics or probability is really an integral. The trick is that they aren't Riemann integrals, but they are a more advanced type called Lebesgue integrals, which has to do with measure theory. The main difference between the two is that a Riemann integral count every area of space the same ([0,1] counts just as much towards your integral as [1,2]), but Lebesgue integrals use what is called a measurable function, which maps f(set) -> positive number. You can use this function to weight different parts of your integral differently. Now what you can do is make measurable functions that map f(set) -> how likely that set happens (which is exactly the probability)