8. When using an atomic force microscope, it is essential that the scope base be as stable as possible. This problem addresses two WSS discrete-time random process models for the vibration, X(k), of the base. a. Assume that X(k) is zero mean white noise with variance 0-; = 9. What is the autocorrelation process RX (m) , and the PSD SK ((0) forX(k)? Now assume that X(k) is a zero-mean, AR process with variance of! = 9. Specifically, assume that: X(k) = 0.8X(k 1)+W(k) where W(k) is a white-noise process. Compute RAD) and RA 1). What is the variance of the white noise process W(k)? If you were to plot a sample realization of both models (from parts a) and b)), which model would you expect to vary more slowly? Explain why