Let {$Z_t$} denote a white noise process with mean zero and variance $^2$. Define the stochastic process {$X_t$} by $$X_t = X_{t-1} + Z_t + Z_{t-1}.$$ Provide the following, each to three decimal places.

Part (a) $E(X_t Z_{t-1})$

Part (b) The variance of {$X_t$}

Part (c) The autocovariance function of {$X_t$} at lag 1.

Part (d) The autocorrelation function of {$X_t$} at lag 2.