( state process that results from Ck+1 = AkXK + Wk, when To, Wo, W1, W2, . . . are independent and jointly Gaussian, is a Markov process and Gaussian. In this problem, you are asked to prove the converse result.) Let xx be a Markov process that is Gaussian. Suppose Eck = 0, and let Ek := cov(Xk), Ek+1,k := cov(k+1, Xk), Show that Ck+Ik : = Eck+1|x ] = Ek+1,KER CCK. Now let Wk := Ck+1 - Ck+1/k. Show that the random variables To, Wo, W1, W2, ... are Gaussian and independent. (This result thus shows that a Gauss Markov process has a representation of the form Ck+1 = Akck + WK, where Ak := Ek+1,KER. ) Hint: Recall that Xx is Markov. Hence Elk+1/2*] = E[aktilack].]