In what follows, $w_t$ always denotes the white noise which is normally distributed about 0, with constant variance $\sigma^2$ and $E(w_t w_s) = 0$ for all $t \neq s$.
2 (4 points) Let $X_t = 5t^2 + t + w_t$. Let $\nabla$ denotes the differencing operator, i.e., $\nabla X_t = X_t - X_{t-1}$.
(a) Show that the stochastic process $Y_t := \nabla^2 X_t$ is covariance stationary.
(b) Describe $Cov(Y_t, Y_{t+h})$ for all integer values of $h \geq 0$.
