PDFs of the observed RG relative total matter density RV given a radio luminosity at ν_ref = 150 MHz, using MLE parameter values for the model described in Sect. 4.2. The black contours denote CDF values. We overplot all 1443 selected LoTSS DR1 RGs (dots), with those above the empirical median density coloured red, and those below coloured blue. We used flexible voxel method densities. For fixed voxel method densities, see Fig. D.1.