When X and Y have expected values µX = µY = 0, Theorem 9.4 says that
L (Y) =
Show that this result is a special case of Theorem 9.7(a) when random vector Y is the 1- dimensional random variable Y.
Theorem 9.4
Random variables X and Y have expected values µX and µY, standard deviations σX and σY, and correlation coefficient ρ X,Y, The optimal linear mean square error (LMSE) estimator of X given Y is
L (Y ) = a∗Y + b∗ and it has the following properties
![](https://test.transtutors.com/qimg/34df94e4-44a4-4eb5-8fb1-bf5fa62a0466.png)
Theorem 9.7(a)
![](https://test.transtutors.com/qimg/e7dc83c7-46aa-40c4-b21e-6f1af29f5cae.png)