Let {X(t), −∞ < t < ∞} be a weakly stationary process having covariance function RX (s) = Cov[X(t), X(t + s)].

(a) Show that Var(X(t + s) − X(t)) = 2RX (0) − 2RX (t)

(b) If Y (t) = X(t + 1) − X(t) show that {Y (t), −∞ < t < ∞} is also weakly stationary having a covariance function RY (s) = Cov[Y (t), Y (t + s)] that satisfies RY (s) = 2RX (s) − RX (s − 1) − RX (s + 1)