please show the work

(1) Consider the following four ARMA processes, where as usual is WN(0,02): (i) MA(1): Xn=Zn + .75Zn-1 (ii) AR(1): Xn_ .75X,-1 = Zn (iii) ARMA(1,1): Xn_ .75Xn_ 1 =Zm+ .752,-1 (iv) AR(2): Xn_ .75X,-2 = Zn For each of these processes, determine (a) the autocovariance sequence of the process (include a sketch), (b) the spectral density of the process (include a sketch), and (c) the formula for the best linear predictor of Xn+1 in terms of Xn, Xn-1, i.e. calculate

(1) Consider the following four ARMA processes, where as usual Z,, is WN(O, 02): (i) MA(1): X = Zn+.75Z n1 (1i) AR(1): Xn - .75Xn_1 = Z,, (iii) ARMA(1,1): Xn .75X _1 = Z1n + .75Zn_1 (iv) AR(2): X", .75Xn_2 = Z,, For each of these processes, determine (a) the autocovariance sequence of the process (include a sketch), (b) the spectral density of the process (include a sketch), and (c) the formula for the best linear predictor of Xn+1 in terms of Xannl, i.e. calculate Xn+1 = P(Xn+1|Xn;Xnml)