scatter in the [${\mathcal{M}_\mathrm{bh}}$]{}–[${\mathcal{M}_*}$]{} relation. It does not indicate that SMBH masses are intrinsically higher in AGN host galaxies. Finally, the evolution in the normalization of the XLF is explained by a rapid drop in the probability of a galaxy hosting an AGN at later times for all specific accretion rates and across all stellar masses.

Discussion {#sec:discuss}
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We have shown how with a simple, observationally motivated model we are able to explain the predominant features of the XLF of AGNs and its evolution over $0.2<z<1.0$. We start with the observed SMF of galaxies (and its very mild evolution) from PRIMUS [@Moustakas13] and populate these galaxies with AGNs based on a model for the probability of hosting an AGN as a function of specific accretion rate. Our model is based on the observations at low-to-moderate accretion rates (equivalent to Eddington ratios $\sim10^{-3}-0.1$) and over a wide range of stellar masses ($9.5<\log {\mathcal{M}_*}/{\mathcal{M}_{\sun}}<12$) from @Aird12. We extend our model to higher accretion rates (equivalent to Eddington ratios $\gtrsim0.1$) using a small number of straightforward assumptions. Our final model has one free parameter—the slope of the distribution at super-Eddington accretion rates—which we fit using the observed bright end of the XLF. 