For the modelX=+W, and under the usual independence and normality assumptions forandW, the mean squared error of the LMS estimator is

1(1/₀²)+(1/₁²),

where₀²and₁²are the variances ofandW, respectively.Suppose now that we change the observation model toY=3+W. In some sense the "signal"has a stronger presence, relative to the noise termW, and we should expect to obtain a smaller mean squared error. Suppose₀²=₁²=1. The mean squared error of the original modelX=+Wis then1/2. In contrast, the mean squared error of the new modelY=3+Wis _____?

Hint:Do not solve the problem from scratch. Think of an alternative observation model in which you observeY=+(W/3)

.