Solution
= Solution
Writing the <log-likelihood> as $\ell(\beta)=\log L(\beta)$, the <Fisher information matrix> is the expected negative <Hessian matrix>
$$
\boxed{\mathcal I(\beta)=-\mathbb E_\beta\!\left[\nabla_\beta^2\ell(\beta)\right].}
$$
Under the usual regularity conditions it is equivalently the expected outer product of the <score function>.