Some features of the absorption and luminescence spectra of excitons in disordered 2D semiconductors appear to be nearly universal over a wide range of samples. In particular, the offset of the peaks of these two spectra is proportional to their linewidths, over a range of two orders of magnitude. The authors show that the relationship between these spectra can be understood in terms of the statistical properties of a Gaussian random function: the absorption spectrum is proportional to the probability distribution of the function itself, whereas the luminescence spectrum is proportional to the distribution of the heights of the minima of the function.