2. Consider the simple linear regression model:
$y_t = \beta y_{t-1} + \varepsilon_t,$
with the error structure as below:
$\varepsilon_t = \rho \varepsilon_{t-1} + u_t,$
where $u_t \sim i.i.d(0, \sigma^2)$. What is the probability limit ($\rho$ lim) of OLS estimator $\hat{\beta}$?      (2)      
(A). \( \frac{\beta}{1 + \beta\rho} \)
(B). \( \beta \)
(C). \( \frac{\beta + \rho}{1 + \beta\rho} \)
(D). \( \frac{\rho}{1 + \beta\rho} \)
(E). \( \frac{1}{1 + \beta\rho} \)

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