# Derivation of conditional expectation and variance of the AR(1) process [duplicate]

I have a question regarding the AR(1) process. I want to derive the conditional expectation $$E(X_{(t)}| X_{(0)})$$ and the variance $$\operatorname{Var}(X_{(t)}|X_{(0)})$$ of the AR(1) process: $$X(t)=aX(t-1)+Z(t)$$ Where $$Z(t)$$ is i.i.d. normally distributed with standard deviation $$b$$. Does anyone knows how to do it?

• Have you looked at related questions on this site? There might be quite a few relevant ones. Oct 16 '15 at 14:33