Cumulative distribution function (CDF) of bolometric (black) and hard X-ray (2 − 10 KeV, red) luminosity of LISA detectable (S/N > 10) MBHBs with masses M_Bin > 10⁵ M_⊙. Darker lines correspond to the Loud model whereas the light curves depict the predictions of the Quiet one. Horizontal lines highlight the CFR values of 0.5 and 0.2. The vertical pink line highlights the luminosity value of 10⁴³ erg s⁻¹, while black dashed and dotted lines represent the minimum luminosity that a source must have respectively at z = 1 and z = 0.5 to be detected by Athena X-ray observatory assuming a flux limit in the hard X-ray of 2 × 10⁻¹⁵ erg s⁻¹ cm⁻² (see Lops et al. 2023).