1. (1) Let y(t) be a time series with a constant mean E(y(t))=m. Show that the sample mean is an unbiased estimator for m.
(2) Let y(t) be a time series with a constant mean E(y(t))=m, constant variance var(y(t)), and
cov(y(t),y(j))=0 for t not equal to j. Show that the variance of the sample mean is var(y(t))/T.