And let's say that Y is equal to the number of hours that same person, person was awake yesterday. And appreciate why these are not independent random variables. One of them is going to completely determine the other. If I slept eight hours yesterday, then I would have been awake for 16 hours. If I slept for 16 hours, then I would have been awake for eight hours. We know that X plus Y, even though they're random variables, and there could be variation in X, and there could be variation in Y, but for any given person, remember, these are still based on that same person, X plus Y is always going to be equal to 24 hours. So these are not independent, not independent.