The soft X-ray properties of quasars in the Sloan Digital Sky Survey
  We use the ROSAT All Sky Survey (RASS) to study the soft X-ray properties of a homogeneous sample of 46,420 quasars selected from the third data release of the Sloan Digital Sky Survey (SDSS). Optical luminosities, both at rest-frame 2500\AA ($L_{2500}$) and in [OIII] ($L_{[\rm{OIII}]}$) span more than three orders of magnitude, while redshifts range over $0.1<z<5.4$. We detect 3366 quasars directly in the observed 0.1--2.4 keV band. Sub-samples of radio-loud and radio-quiet objects (RLQs and RQQs) are obtained by cross-matching with the FIRST catalogue. We study the distribution of X-ray luminosity as a function of optical luminosity, redshift and radio power using both individual detections and stacks of complete sets of similar quasars. At every optical luminosity and redshift $\log L_{2\kev}$ is, to a good approximation, normally distributed with dispersion $\sim 0.40$, at least brightwards of the median X-ray luminosity. This median X-ray luminosity of quasars is a power law of optical luminosity with index $\sim 0.53$ for $L_{2500}$ and $\sim 0.30$ for $L_{[\rm{OIII}]}$. RLQs are systematically brighter than RQQs by about a factor of 2 at given optical luminosity. The zero-points of these relations increase systematically with redshift, possibly in different ways for RLQs and RQQs. Evolution is particularly strong at low redshift and if the optical luminosity is characterised by $L_{[\rm{OIII}]}$. At low redshift and at given $L_{[\rm{OIII}]}$ the soft X-ray emission from type II AGN is more than 100 times weaker than that from type I AGN. 
Shiyin Shen, Simon D.M. White, H.J. Mo, Wolfgang Voges, Guinevere   Kauffmann, Christy Tremonti, Scott F. Anderson