My professor wrote an equation out in class on the board that I wrote and didn't really look at until days later. The equality was this:
$P(Y<a)=E[P(Y<a|X))]$
What conditional expectation theorem is this? It's weird taking the expected value of a probability rather than a random variable even though I know that its logically makes sense once I stop to think about it.
What assumptions do I have to make to use this theorem?