117

  : Number of selected SDSS DR7 and DR9 QSOs found in HeRS, HeLMS, Boötes, Lockman-SWIRE and [*XMM*]{}-LSS regions. The Lockman-SWIRE field does not overlap with the DR9 quasar sample and the [*XMM*]{}-LSS field does not overlap with the DR7 quasar sample. Note that the number of DR9 QSOs in the HeRS and HeLMS Stripe 82 regions goes through a final change in Section 3.2. The numbers inside the brackets represent the final number of DR9 quasars in these two regions. The median redshift for the DR7 and DR9 QSOs is 1.4 and 2.5, respectively.

In the left panel in Fig. \[fig:dndz\_mi\], we plot the normalised redshift distribution of the SDSS DR7 and DR9 QSO samples. The dashed lines correspond to the normalised redshift distribution of the entire DR7 and DR9 QSO samples, while the solid lines correspond to the selected QSO samples used in the cross-correlation analysis. Compared to the expected redshift distribution of the integrated sub-mm emission at 250, 350 and 500 $\micron$ from various models (Valiante et al. 2009; Bethermin et al. 2011; Bethermin et al. 2012; Viero et al. 2013), we can see that the SDSS DR7 and DR9 quasars completely cover the redshift range where 