Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 28K / a / Solution

{title2=$I(\theta)=\Sigma^{-1}$}

For $X\sim N_p(\theta,\Sigma)$ with known nonsingular covariance matrix, the <score function> is $\Sigma^{-1}(X-\theta)$ and the per-observation <Fisher information matrix> is $\Sigma^{-1}$. In particular, covariance $I_p$ gives information $I_p$.

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 Incoming links: Fisher information of a multivariate normal location model