b. Recall that at time t the Poisson process N(t) is a Poisson random variable with parameter Xt. We can think of N(t) as counting the number of points in an interval (0, t] if we start at 0 as the origin (the meaning of these points depends on the application). Now define a new random process as X (t) = 1 if N(t) is even and X(t) = -1 if N(t) is odd. Note that N(0) = 0 so X(0) = 1. i. Compute E[X(t)]. Simplify your result as much as possible. = == ii. As noted above X(0) 1 (since N(0) = 0) and is not random. To remove this certainty we form a new random process Y(t) = A X(t) where A is a random variable taking values +1 and -1 with equal probability. One can show that Y(t) is WSS with covariance function Ky(T) = e2|7|. Determine (mathematically) whether or not Y(t) is ergodic in mean.