I have finally just proved the sampling distribution of the estimated regresion mean $\displaystyle \hat{\alpha} + \hat{\beta}x_{0}$

as

$\displaystyle \hat{\alpha} + \hat{\beta}x_{0} \sim N (\alpha + \beta x_{0} , \sigma^{2} \{ \frac{1}{n} + \frac{(x_{0}-\bar{x})^2}{S_{xx}} \})$

After all that I now have been asked to comment on the parameters and estimated values about which are fixed quantities and which are random variables, but from all my work proving the formula I have got myself completely confused on this commenting section.

Please help