Observed redshift (z_spec) vs. modeled redshift (z_model) to optimize H₀. To demonstrate how z_model depends on H₀, we present three values of H₀, 60, 68, and 80 km s⁻¹ Mpc⁻¹, in the different panels. We used 30 FRBs (see Sect. 4 and Table 1 for details) with DM_h = [20, 1600] pc cm⁻³ and $A_{\tau }\stackrel{\sim }{F}G=[0.001,10]$${({\mathrm{pc}}^2\mathrm{km})}^{-\frac{1}{3}}$. The black line corresponds to z_model = z_spec.