= Solution
A constant <improper prior> would give the formal <posterior density> kernel $N^{-1}\mathbf1_{\{N\geq y\}}$. However,
$$
\sum_{N=y}^{\infty}\frac1N=\infty.
$$
\b[There is no normalized posterior distribution under this prior.] The failure is not simply that the <prior> is improper: some improper priors give proper posteriors. Here <posterior propriety> itself fails after this single observation, so probabilities, quantiles and a <posterior mean> cannot be assigned to that kernel.
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