These extreme values are two away from the 12. And this is just to give us an intuition. Once again, it's not a rigorous proof. So it actually turns out that in either case, when you're taking the variance of X plus Y or X minus Y, you would sum the variances, assuming X and Y are independent variables. Now with that out of the way, let's just calculate the standard deviation of X plus Y. Well, we know this. Let me just write it using this sigma notation.