= Solution
{c}
For a scalar <statistical parameter> in a regular model with <probability mass function> $f(x\mid\theta)$, define the one-observation expected <Fisher information> by
$$
I(\theta)=\mathbb E_\theta\!\left[\{\partial_\theta\log f(X\mid\theta)\}^2\right]
=\sum_x\frac{\{\partial_\theta f(x\mid\theta)\}^2}{f(x\mid\theta)}.
$$
The <Jeffreys prior> is the <prior density> specified, up to a factor independent of $\theta$, by
$$
\boxed{\pi_J(\theta)\propto\sqrt{I(\theta)}.}
$$
For $n$ independent observations the <Fisher information> is $nI(\theta)$, so the factor $\sqrt n$ does not change this <prior distribution>. If $\int\sqrt{I(\theta)}\,d\theta$ is finite, divide by this integral to normalize; otherwise the rule defines an <improper prior>.
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