When x and y have expected values microxnbsp microynbsp 0

Question

When X and Y have expected values µ_X = µ_Y = 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 µ_X and µ_Y, standard deviations σ_X and σ_Y, 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

Theorem 9.7(a)