Solution
= Solution
Since $\widehat\beta=\beta^0+(X^TX)^{-1}X^T\varepsilon$ and $\operatorname{cov}(\varepsilon)=\sigma^2I_n$,
$$
\boxed{\operatorname{cov}(\widehat\beta)
=\sigma^2(X^TX)^{-1}}.
$$
= Solution
Since $\widehat\beta=\beta^0+(X^TX)^{-1}X^T\varepsilon$ and $\operatorname{cov}(\varepsilon)=\sigma^2I_n$,
$$
\boxed{\operatorname{cov}(\widehat\beta)
=\sigma^2(X^TX)^{-1}}.
$$