Exchangeable random variables

Imagine you have a toy box with different colored balls inside. Each ball represents something you want to pick. Now, let's say you close your eyes and pick two balls at random.

If you pick one ball, put it back in the toy box, shuffle it around and then pick the second ball without looking at what you previously picked, these two picks are called exchangeable random variables.

In math, exchangeable random variables are when the order in which you pick them doesn't matter. It's like the balls in the toy box, whether you picked them first or second, they are still random and equally important.

So, if you have a group of exchangeable random variables, you can rearrange them in any order and they will have the same probability of being picked. It's like shuffling a deck of cards or picking different colored marbles out of a jar. As long as you keep the number and properties of the items the same, it doesn't matter what order you pick them in.