OLS - Why coefficient Beta has Normal Distribution but not t-Distribution I have a little trouble understanding the solution to the following problem. To my understanding, coefficients in OLS should follow t-distribution. However, the solution says it follows Normal.
Please see the answer in the picture


In OLS, we typically assume the following for the error terms $u$:

*

*A(1): $ E(u) = 0 $

*A(2): $ u \sim N(0, \sigma^2I) $
this leads to the distribution $ \widehat{\beta} \sim N(\beta, \operatorname{Var}(\widehat{\beta})) $ in small samples, if assumption A(2) holds true and even approximate for large samples, if A(2) is violated
