Supposeare two jointly Gaussian random variables considered in the earlier example. We have to estimate from a single observation .The MMSE estimator is given by
If and then
Thus the MMSE estimator for two zero-mean jointly Gaussian random variables is linearly related with the data . This result plays an important role in the optimal filtering of random signals.
are two jointly Gaussian random variables considered in the earlier example. We have to estimate 
from a single observation 
.The MMSE estimator 
is given by 
and 
. This result plays an important role in the optimal filtering of random signals.