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)