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Consider the

`AR(1)`

series

`x_(t)=\phi x_(t-1)+w_(t),`

where

`w_(t)`

is white noise with variance

`\sigma _(w)^(2)`

and the model parameters are known. Suppose that we have observed

`x_(1)`

and

`x_(3)`

, and we would like to estimate the missing value

`x_(2)`

. Find the best linear predictor of

`x_(2)`

in terms of

`x_(1),x_(3)`

and

`\phi `

.