If X is completely independent of Y, and if I have some random variable that is the sum of the two, then the expected value of that variable, of that new variable, is going to be the sum of the expected values of the other two, because they are unrelated. If I think, if my expected value here is 5 and my expected value here is 7, it's completely reasonable that my expected value here is 12, assuming that they are completely independent. Now, if we have a situation, so what is the variance of my random variable Z? And once again, I'm not going to do a rigorous proof here, this is really just a property of variances, but I'm going to use this to establish what the variance of our random variable A is. So if this squared distance on average is some variance, and this one is completely independent, and its squared distance on average is some distance, then the variance of their sum is actually going to be the sum of their variances. So this is going to be equal to the variance of random variable X plus the variance of random variable Y. So another way of thinking about it is that the variance of Z, which is the same thing as the variance of X plus Y, is equal to the variance of X plus the variance of random variable Y.