Suppose you want to determine an unknown DC voltage vdc in the presence of addi- tive white Gaussian noise n(t) of zero mean and variance 0% 12. The measured signal is x(t) = vde+n(t). An estimate of vde is computed by making three independent measure- ments of x(t) and computing the arithmetic mean, Vdc (x1+x2+x3)/3.

(a) Find the mean and variance of the random variable Vdc

(b) Does the estimate of vac get better by using ten measurements instead of three? Why?