Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 219 / 1 / a / Solution

For distinct sibling supernovae $s$ and $s^{\prime }$ in the same galaxy, the shared fluctuation is the only common random term. Independence and linearity of covariance therefore giveTheir correlation coefficient isThis is the intraclass correlation coefficient of the galaxy-level random intercept model.