please solve this problems Consider the following autoregressive processes: W 2W-1X Wo 0 Zn = 3/4 Zq-1 + Xn Zo = 0. (a)...
Consider the following autoregressive processes: W 2W-1X Wo 0 Zn = 3/4 Zq-1 + Xn Zo = 0. (a) Suppose that Xn is a Bernoulli process. What trends do the processes exhibit? (b) Express Wn and Zn in terms of Xn, Xn-1, ..., X1 and then find E[Wn] and E[Zn]. Do these results agree with the trends you expect? (c) Do Wn or Zn have independent increments? stationary increments? (d) Generate 100 outcomes of a Bernoulli process. Find the resulting realizations of Wn and Zn. Is the sample mean meaningful for either of these processes? (e) Repeat part d if Xn is the random step process.
Consider the following autoregressive processes: W 2W-1X Wo 0 Zn = 3/4 Zq-1 + Xn Zo = 0. (a) Suppose that Xn is a Bernoulli process. What trends do the processes exhibit? (b) Express Wn and Zn in terms of Xn, Xn-1, ..., X1 and then find E[Wn] and E[Zn]. Do these results agree with the trends you expect? (c) Do Wn or Zn have independent increments? stationary increments? (d) Generate 100 outcomes of a Bernoulli process. Find the resulting realizations of Wn and Zn. Is the sample mean meaningful for either of these processes? (e) Repeat part d if Xn is the random step process.