Nine examples representing the PDFs of redshift (z). These were randomly selected from our FRB samples (see Sect. 4 and Table 1 for details). H₀ = 74.3 km s⁻¹ Mpc⁻¹ and DM_h = [20, 1600] pc cm⁻³ were adopted. In each panel, we present PDFs based on two different ranges of $A_{\tau }\stackrel{\sim }{F}G$: [0.5, 2] (orange line) and [0.001, 10] (blue line) ${({\mathrm{pc}}^2\mathrm{km})}^{-\frac{1}{3}}$. The vertical dashed black line shows the observed redshift (z_spec) in each panel.