Notes. The simulation assumes γ = 0.6 and β = 8.0, with a dispersion of the L_X − L_UV relation of δ = 0.24. The distances have been computed assuming a spatially flat ΛCDM model with Ω_M = 0.1 and Ω_Λ = 0.9 (see Section 6 for details). The ΛCDM model has Ω_M and Ω_Λ free to vary for models 1 and 3, whilst models 2 and 4 have the matter and energy parameters fixed to the values 0.3 and 0.7, respectively. Models 3 and 4 assume an evolution with redshift of both slope and intercept of the X-ray to UV relation in the form: γ(z) = γ₀ + γ₁(1 + z) and β(z) = β₀ + β₁(1 + z). In all models, Ω_k is fixed to zero (spatially flat case) and Ω_r = 2.47 × 10⁻⁵ h⁻², with h = 0.7 km s⁻¹ Mpc⁻¹, Ω_r = 1 − Ω_M − Ω_Λ, and Ω_Λ < 0.99 + 1.8 Ω_M. The latter condition has been enforced to exclude solutions with no Big Bang. Models 5 and 6 are the same as 2 and 4, respectively, but with matter and energy parameter values fixed to Ω_M = 0.9 and Ω_Λ = 0.1. Model 3 is a sanity check to test what happens when the cosmological parameters are free to vary and an evolution of the correlation parameters is allowed.