Solution (source code)

= Solution

Yes. Even under random orientation, a population concentrated at one nonzero intrinsic ratio $q_0$ has
$$
\mathcal P(Q)=
\frac{Q}{\sqrt{1-q_0^2}\sqrt{Q^2-q_0^2}},
\qquad q_0<Q<1,
$$
which decreases from an integrable divergence at the lowest allowed value $Q=q_0$. It is therefore skewed toward the lower end of its support. More generally, a sufficiently narrow intrinsic distribution can retain such low-$Q$ peaks after the mixture in part d.

If the random-orientation assumption is relaxed, preferentially edge-on selection makes $\cos i$ concentrate near zero and hence makes $Q$ concentrate near $q$. Dust extinction, surface-brightness selection, or alignment by environment can instead bias the sample in either direction. Triaxial or prolate galaxy shapes also invalidate the <projected axis ratio of an oblate spheroid> formula and can produce other low-$Q$ distributions.