3. Let X [t] be a discrete-time Bernoulli random process composed of in- dependent Bernoulli random variables, X[t] c {-1, 1}, where P(X [t] = 1) = p. A new random process is constructed by Y [t] = X[t] - X[t-1]. Find the autocorrelation function ry [t + 7, t]. Is Y[t] a WSS process? Solution: For the autocorrelation function of Y [t], we can write ry t+ 7, t] = E( Y [ t + + ]Y[t]) = E((X t+ +] - X[t+ +- 1])(X[t] - X[t - 1])) = rx(t+ 7, t] - rx[t+ 7, t- 1] -rx[t +7 - 1, t] + rx[t+7 - 1, t - 1]. For rx [t + T, t) we can write rxt + 7, t = (2p - 1)2, 10 1 , T = 0