Homework SourseStart with the defintion of the covariance of X and Y and sh
Start with the defintion of the covariance of X and Y and show the steps necessary such that it can be written as E[XY] - E[X] E[Y]
Solution
Covariance of xy = E(x- x bar)(Y-ybar)
This can be simplified as
Cov (x,y) = E[xy- xybar-yxbar+xbarybar]
= E(xy) -E(xybar)-E(yxbar)+E(xbarybar)
x bar and y bar are constant and can be taken out
= E(xy) - ybarE(x) -x bar E(y)+xbar ybar
= E(xy) -xbar ybar-xbar ybar+xbar ybar
=E[XY] - E[X] E[Y]
![Start with the defintion of the covariance of X and Y and show the steps necessary such that it can be written as E[XY] - E[X] E[Y]SolutionCovariance of xy = E(](/WebImages/23/start-with-the-defintion-of-the-covariance-of-x-and-y-and-sh-1057847-1761552159-0.webp "Start with the defintion of the covariance of X and Y and show the steps necessary such that it can be written as E[XY] - E[X] E[Y]SolutionCovariance of xy = E(")
