4. Consider an AR(1) model Y = Bo+B-1+u. Suppose the process is stationary. (a) What do we know about the value of the slope coefficient B? Explain. (b) Explain why E(Y) = E(Y-1) and Var(Y) = Var(Y-1). (c) Prove that E(Y) = Bo 1-B (d) Suppose the model is Y = 2.5+.7Y-1+u where E(u) = 0; Var(u) = 9. Calculate the follow- ing quantities: the mean and the variance of Y,, i.e. E(Y) and Var(Y) the 1st autocovariance and autocorrelation coefficient of Y. Hint: you can use without proving the fact that Cov(ax + bY + cZ,T) = aCov(X,T)+bCov(Y,T)+cCov(Z,T) and Cov(X,X)=Var(X) where X,Y,Z, and T are random variables.