And really it's just kind of a fun math thing to do to show you all of these connections and where really the definition of covariance really becomes useful. And I really do think it's motivated to a large degree by where it shows up in regressions. And this is all stuff that we've kind of seen before. You're just going to see it in a different way. So this whole video I'm just going to rewrite this definition of covariance right over here. So this is going to be the same thing as the expected value of, and I'm just going to multiply these two binomials in here. So the expected value of our random variable X times our random variable Y minus, well I'll just do the X first.