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. If you're given one of the variables, it would completely determine what the other variable is. The probability of getting a certain value for one variable is going to be very different given what value you got for the other variable. So they're not independent at all.