Suppose you want to determine an unknown DC voltage vdc in the presence of
additive white Gaussian noise n(t) of zero mean and variancesn 2 . The measured
signal is x(t) = vdc + n(t). An estimate of vdc is computed by making three independent measurements of x(t) and computing the arithmetic mean,
 v
dc ≈ (x1 + x2
+ x3)/3. (a) Find the mean and variance of the random variable
 v
dc . (b) Does the
estimate of vdc get better by using ten measurements instead of three? Why?