# Math Help - Limit distribution

1. ## Limit distribution

Hello,

I want to find the asymptotic distribution of $\hat{\beta}$. And this happens to be the sum of two normally distributed terms. i.e.

$\sqrt{n}(\hat{\beta} - \beta) = X-Y$

Where,

$X \longrightarrow N(0, \sigma^2 )$

$Y \longrightarrow N(0, \omega^2 )$

__________________________________________________

So is this correct:

$\sqrt{n}(\hat{\beta} - \beta) \longrightarrow N(0, \sigma^2 + \omega^2)$

??