need help with this problem, please include r code

6.1 Consider a system process given by x; = .9xt_2 +wt t=1,...,n where x0 ~ N(0, 0'3), xi] ~ N (0, 0-12), and w, is Gaussian white noise with variance 0%,. The system process is observed with noise, say, )7: = xr +Vt, where v, is Gaussian white noise with variance 0'3. Further, suppose x0, x_1, {wt} and {VI} are independent. (a) Write the system and observation equations in the form of a state space model. (b) Find the values of 0-3 and 0-]2 that make the observations, 32,, stationary. (c) Generate n = 100 observations with (7w = 1, (7,, = 1 and using the values of 06,2 and 0-12 found in (b). Do a time plot of x, and of y, and compare the two processes. Also, compare the sample ACF and PACF of x; and of y;. ((1) Repeat (0), but with 0-,, = 10