Eddington ratio distribution of the X-ray AGN within three redshift bins. On the left panels we plot the perfect-sky distribution and on the right panels the distribution after all observational and XMM-Newton instrumental effects were simulated (10 ks exposures, see Sect. 3.3). To illustrate observational selection effects, we overplot deep observational data on the perfect-sky distribution, and shallow on the 10 ks exposures (see Sect. 4.2 for more discussion).