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We investigate the dispersion measure(DM) and scattering of FRBs by theintergalactic-medium(IGM), foreground and host halos, using cosmologicalhydrodynamical simulation. We find that the median DM caused by foregroundhalos is around 30\% of that caused by the IGM, but has a much larger variance.The DM induced by hosts deviates from a log-normal distribution, but exhibitsan extended distribution in the range of $1-3000 \ {\rm{pc\, cm^{-3}}}$ with amedian value $\sim 100 \ {\rm{pc\, cm^{-3}}}$. Then we produce mock FRBsources, assuming a uniform distribution in the range $z\sim 0-0.82$, toconsider the propagation effect of IGM, foreground and host halos on FRBsignals simultaneously. The DM distribution of mock sources agrees well withthe observation. The fitted DM-redshift relation of the mock sources canprovide a rough estimation of the redshifts of observed events with errors$\delta z \lesssim 0.15$. The distribution of mock sources in the DM-scatteringtime($\tau$) space can also match the observation, assuming a Kolmogorovturbulence model with the inner and outer scale is 1000 km to 1 AU, and 0.2-10pc respectively. Finally, we estimate the relative importance of these mediumon DM and $\tau$ in our models. The IGM and host halos are the primary andsecondary sources to the extragalactic DM, $\rm{DM_{exg}}$. Meanwhile, thecontribution from foreground halos increases as $\rm{DM_{exg}}$ increases. Thehost and foreground halos may be the most important medium for scattering.Statistically, the latter may dominate the scattering of events with$\rm{DM_{exg}} \gtrsim 200 \ {\rm{pc\, cm^{-3}}}$.

The dispersion measure and scattering of FRBs: Contributions from the intergalactic medium, foreground halos, and hosts