= Solution
For a regular scalar <statistical model>, the one-observation <Fisher information> is
$$
I(\theta)=\mathbb E_\theta\!\left[
\left\{\partial_\theta\log p(Y\mid\theta)\right\}^2\right].
$$
Under the usual differentiation and interchange-of-integral conditions it also equals $-\mathbb E_\theta[\partial_\theta^2\log p(Y\mid\theta)]$. The <Jeffreys prior> is
$$
\boxed{p_J(\theta)\propto\sqrt{I(\theta)}.}
$$
This prior measure is invariant under smooth one-to-one reparameterization, but may be improper. For independent identically distributed observations the information multiplier $n$ changes only the prior's proportionality constant.
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