  High time resolution radio surveys over the last few years have discovered a
population of millisecond-duration transient bursts called Fast Radio Bursts
(FRBs), which remain of unknown origin. FRBs exhibit dispersion consistent with
propagation through a cold plasma and dispersion measures indicative of an
origin at cosmological distances. In this paper we perform Monte Carlo
simulations of a cosmological population of FRBs, based on assumptions
consistent with observations of their energy distribution, their spatial
density as a function of redshift and the properties of the interstellar and
intergalactic media. We examine whether the dispersion measures, fluences,
inferred redshifts, signal-to-noises and effective widths of known FRBs are
consistent with a cosmological population. Statistical analyses indicate that
at least 50 events at Parkes are required to distinguish between a constant
co-moving FRB density, and a FRB density that evolves with redshift like the
cosmological star formation rate density.
