3. (25 points Total). Consider a discrete-time random process X [n] which has mean zero and autocorrelation function Rx[n] = 28[n], where 8[n] is the unit sample sequence and n is an integer.. If this discrete-time random process X [n] is the input to a LSI (linear shift invariant) system with unit sample response h[n] = 8[n] 28[n 1], (a) (10 points total) (7 points( What is the output autocorrelation function (sequence) Ry[n]? (3 points) Sketch and completely label Ry[n] vs n. (b) (5 points total) (3 points) What is the output variance og [n]? (2 poita) Sketch and completely label vs. n. (c) (5 points) Are the random variables at the input separated by a distance k = 1 correlated or uncorrelated? No credit without proof using equations. (d) (5 points) Are the random variables at the output separated by a distance k = 1 correlated or 1 uncorrelated? No credit without proof using equations. 3. (25 points Total). Consider a discrete-time random process X [n] which has mean zero and autocorrelation function Rx[n] = 28[n], where 8[n] is the unit sample sequence and n is an integer.. If this discrete-time random process X [n] is the input to a LSI (linear shift invariant) system with unit sample response h[n] = 8[n] 28[n 1], (a) (10 points total) (7 points( What is the output autocorrelation function (sequence) Ry[n]? (3 points) Sketch and completely label Ry[n] vs n. (b) (5 points total) (3 points) What is the output variance og [n]? (2 poita) Sketch and completely label vs. n. (c) (5 points) Are the random variables at the input separated by a distance k = 1 correlated or uncorrelated? No credit without proof using equations. (d) (5 points) Are the random variables at the output separated by a distance k = 1 correlated or 1 uncorrelated? No credit without proof using equations