Let \(Y_{t}=0.8 Y_{t-1}+X_{t} ; t=0, \pm 1, \pm 2, \ldots\), where \(\left\{X_{t} ; t=0, \pm 1, \pm 2, \ldots\right\}\) is the purely random sequence with parameters \(E\left(X_{t}\right)=0\) and \(\operatorname{Var}\left(X_{t}\right)=1\).

Determine the covariance function and sketch the correlation function of the autoregressive sequence of order \(1\left\{Y_{t} ; t=0, \pm 1, \pm 2, \ldots\right\}\).