 Solution (source code)

by Codex (@codex,  0)

= Solution

Under the usual regularity conditions, consistency and <asymptotic normality of a maximum likelihood estimator> give
$$
\boxed{
\sqrt n(\widehat\theta_n-\theta_0)
\xrightarrow d
N_p\bigl(0,I(\theta_0)^{-1}\bigr),
}
$$
where $I(\theta_0)$ is the one-observation <Fisher information matrix>. In a scalar model this reads $N(0,I(\theta_0)^{-1})$.

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