Let {Y_t} be the AR(1) plus noise time series defined by Y_t = X_t + W_t, where {W_t} ~ WN(0, sigma_w^2), {X_t} is the AR(1) process of Example 2.2.1, i.e., X_t - phi*X_{t-1} = Z_t, {Z_t} ~ WN(0, sigma_z^2), and E(W_s*Z_t) = 0 for all s and t. a. Show that {Y_t} is stationary and find its autocovariance function. b. Show that the time series U_t := Y_t - phi*Y_{t-1} is 1-correlated and hence, by Proposition 2.1.1, is an MA(1) process. c. Conclude from (b) that {Y_t} is an ARMA(1,1) process and express the three parameters of this model in terms of phi, sigma_w^2, and sigma_z^2.