What is $Cov(X_t , X_{t-2})$ based on $Var({X_t})$ in model $AR(1)$. I tried using $X_t - \mu = a(X_{t-1} - \mu) + Z_t$ to find $X_{t-2}$ based on $X_t$ as fallow $$ X_{t-2} = \frac{X_t - \mu - aZ_{t-1} - Z_t+a^2\mu}{a^2}$$ and then solving $Cov(X_t , X_{t-2})$ and i reach to something like $$\frac{1}{a^2}Var(X_t) - \frac{1}{a}E[X_tZ_{t-1}] - \frac{1}{a^2}E[X_tZ_{t}]$$ but is coud i write $- \frac{1}{a}E[X_tZ_{t-1}] - \frac{1}{a^2}E[X_tZ_{t}]$ based on $Var({X_t})$ or it might be the case that question is wrong!?
2026-03-30 10:11:32.1774865492
$Cov(X_t , X_{t-2})$ in $AR$ model.
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