In this section we present a simple, observationally motivated model to populate galaxies with AGNs. We start with our measurements of the galaxy SMF and convolve with a model for the probability of hosting an AGN as a function of specific accretion rate. This convolution provides us with a prediction for the XLF of the AGN population, which we can compare with the observations. Our model for the XLF can be expressed as $$\begin{aligned}
\psi(L_\mathrm{X}, z) & =  & \phi({\mathcal{M}_*}, z) * p(\lambda {\;|\;}{\mathcal{M}_*},z) \\
                   & = & \int \phi({\mathcal{M}_*}, z) \; p\big( \lambda(L_\mathrm{X}, {\mathcal{M}_*}) {\;|\;}{\mathcal{M}_*},z\big) {\;\mathrm{d}}\log {\mathcal{M}_*}\nonumber\end{aligned}$$ where $\phi({\mathcal{M}_*}, z)$ is the galaxy SMF and $p(\lambda {\;|\;}{\mathcal{M}_*},z)$ describes the probability density per logarithmic $\lambda$ interval for a galaxy of given [${\mathcal{M}_*}$]{} and $z$ hosting an AGN with a specific accretion rate, $\lambda$.[^1] This equation allows us to predict the XLF, $\psi(L_\mathrm{X}, z)$, assuming the luminosity-dependent bolometric corrections of @Hopkins07b to convert from $\lambda$ to an X-ray luminosity, $L_\mathrm{X}$, for a given [${\mathcal{M}_*}$]{}. In Figure \[fig:accdists\] we show our three models for $p(\lambda {\;|\;}{\mathcal{M}_*},z)$, all of which are based on the power-law distribution measured by @Aird12 that is independent of stellar mass but evolves strongly with redshift (see Equation \[eq:pldist\] 