Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 320 / 1 / g / Solution

For an ordinary intrinsic density, inversion of the Abel transform givesIf $\mathcal{P}(Q)=1$, the integral is $\pi /2$ for every $q>0$, so its derivative vanishes. The missing probability is an endpoint atom: all systems must be infinitely thin,Indeed, putting $q=0$ directly into part c gives $\mathcal{P}(Q\mid 0)=1$. Thus a uniform apparent-axis-ratio distribution corresponds to a Dirac delta distribution of ideal zero-thickness disks, rather than to a regular intrinsic density.