Please help me to get solutions for the question below.

(X, ) is a stationary ARMA(1.2) time series defined at integer times by the relationship: X, =QX,_+2, + BZ,_2 where cr, f are constants and (7, ) is a purely random process with mean ( and constant variance o . (i) Define the term "(weakly) stationary". [2] (ii) Assuming that the above process has a very long history, what conditions on or and / ensure that it is (a) stationary. and (b) invertible? [2] (iii) Show that for any integer s : cov(X, .Z,)=0' cov(X, Z,_1)=00' cov(X,.Z,_2)= (a-+8)02 (3] (iv) Let yx denote the autocovariance at lag k , ie Y, = cav( X,, X,_;). (a) By considering cov( X,, X,), cov(X,, X,_,) and cov(X,, X,-2), write down luce equations involving yo , 71 and yz. (b) Hence find expressions for 70, y, and y, in terms of the parameters u , A and o' [7] (v) Let p. denote the autocorrelation at lag & . (a) Calculate the values of Po, Pis p2 and py in the case where a - -0.4 and / = -0.9. (b) Hence sketch a graph of the autocorrelation function p for lags k =0.1.2.....10 in this case. (5] [Total 19]