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Let W[n] be an independent random sequence with mean 0 and variance defined for −∞ < n < +∞. For appropriately chosen ρ, let the stationary random sequence X[n] satisfy the causal LCCDE X[n] = ρX[n − 1] +W[n], −∞ < n < +∞. (1) Show that X[n − 1] and W[n] are independent at time n. (2) Derive the characteristic function equation Φ X (ω) = Φ X (ρω)Φ W (ω). (3) Find the continuous solution to this functional equation for the unknown function Φ X when W[n] is assumed to be Gaussian. [Note: Φ X (0) = 1.] (4) What is ?