Consider the linear system Ck+1 = AKCk + BRUK + WK yk = Ckick + Uk, where, with dk := (Wk , VK ) , the random variables ro, do, d1, d2 . .. are independent and jointly Gaussian, with To = N(To, Zo), WK = N(0, Qk), VK = N(0, Rk). The difference from the model treated in class is that we will suppose that wk and vk are correlated. Suppose that COV ( WK, Uk) = Sk. Show that the system can be written as Ck+1 = AkXK + Uk + WK, with an appropriate choice of A, u and w, such that To, Wo, W1, . . ., 10, 1, . .., are inde- pendent and Gaussian. Hint: Take Ak = Ak - SkR, Ck, Wk = WK - Sk RK VK.]