2. Let {Xt} be an MAO) sequence with 6 = 0.5 and a2 = 4. a) Write down the rst difference {VXt} of the sequence {Xi} as an M 24(2) model by explicitly wring down its the parameters. b) Obtain an explicit expression for the spectral density function f (w) of {VXt}, where w is the frequency on [0.5, 0.5]. c) Plot the spectral density functions of {Xt} and {VXt}. Comment on the difference in the shapes of the plots. 3. Let {Zt} be a white noise sequence with a2 = 4. In each case below, obtain the explicit expression of the spectral density function of {Xt}. Then plot the spectral density functions of {Zt} and {X t}, and comment on the differences. a) Xt = QZt 13) Xt = (Zt+1 + Zt + Zt1)/\\/ C) Xt = 0.8Zt_1 0.2Zt2 + Zt d) Xt = Zr Ztl e) Xt = 0.1Zt+2 + 0.25Zt+1 + 0.3Zt + 0.25Zt1 + 0.1Zt_2