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?

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