What are multivariate distributions?

A multivariate distribution is like a recipe that tells you how different ingredients (or events) can mix together in all sorts of ways.

Imagine you have a bag of candies, some are red, and some are blue. If you pick one candy at random, the chance it's red or blue is a univariate distribution, just one thing happening. But now imagine that each candy also has a flavor: cherry or lemon. Now, when you pick a candy, both its color and its flavor can vary.

That’s where multivariate distributions come in! They help us understand how two or more things, like color and flavor, can happen together, and what the chances are for each combination.

Think of it as a candy bag with different layers. One layer might be red cherry candies, another blue lemon ones, and so on. A multivariate distribution is like knowing how many of each kind there are, not just how many red or blue candies, but how they match up with flavors.

So instead of guessing what you’ll get, you can say things like: “There’s a good chance I’ll get a red candy,” or even “I might get a blue lemon one!”, and that’s the power of multivariate distributions!