Best-fit parameters vs. input parameters for the simulations of a 1 mCrab source observed for a 100 ks X-IFU observation (R_f = 2, A_Fe = 2, 1 mCrab, 100 ks, so-called configuration 3). Fifty spins are generated with a constant spacing between 0 and 0.995. All other parameters are drawn from uniform distributions within bounds listed in Table 1. Top-left: black hole spin. Top-middle: height of the coronal source. Top-right: photon index of its spectrum. Then downwards, from left-to-right: parameters of the three absorbers: N_H, the ionization (logξ), and the covering factor. Errors are computed at the 90% confidence level for variation of one single parameter. The mean errors for the spin and height of the irradiating source are ∼0.05 and ∼0.18 R_g respectively. The mean errors for all parameters are listed in Table 2. In particular, the power-law index is accurately determined and shows no bias (see Appendix A).