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.
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