= Normal natural-mean parameter ratio estimator
{title2=$\widehat\phi_1=\bar X/\widehat v$}
For independent $N(\mu,v)$ observations with unknown mean and variance, the first natural parameter is $\phi_1=\mu/v$. Its <maximum-likelihood estimator> is $\bar X/[n^{-1}\sum_i(X_i-\bar X)^2]$. The <delta method> and independent asymptotic mean/variance errors give limiting variance $v^{-1}+2\mu^2v^{-2}$ for $\sqrt n(\widehat\phi_1-\phi_1)$. Knowing $v$ removes the second contribution and makes the estimator exactly normal with variance $1/(nv)$.
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