Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 219 / 1 / b / Solution

The common distance modulus of calibrator galaxy $g$ cancels between its supernova and mean Cepheid apparent magnitudes. Their independent intrinsic scatters therefore giveThus $\mathbb{E}{\hat{S}}_2^g=\Delta M$ and $\mathrm{Var}({\hat{S}}_2^g)=V_2$.