  The observed Fast Radio Burst (FRB) population can be divided into one-off
and repeating FRB sources. Either this division is a true dichotomy of the
underlying sources, or selection effects and low activity prohibit us from
observing repeat pulses from all constituents making up the FRB source
population. We attempt to break this degeneracy through FRB population
synthesis. With that aim we extend frbpoppy, which earlier only handled one-off
FRBs, to also simulate repeaters. We next model the Canadian Hydrogen Intensity
Mapping Experiment FRB survey (CHIME/FRB). Using this implementation, we
investigate the impact of luminosity functions on the observed dispersion
measure (DM) and distance distributions of both repeating and one-off FRBs. We
show that for a single, intrinsically repeating source population with a steep
luminosity function, selection effects should shape the DM distributions of
one-off and repeating FRB sources differently. This difference is not yet
observed. We next show how the repeater fraction over time can help in
determining the repetition rate of an intrinsic source population. We simulate
this fraction for CHIME/FRB, and show that a source population comprised solely
of repeating FRBs can describe CHIME/FRB observations with the use of a flat
luminosity function. From the outcome of these two methods we thus conclude
that all FRBs originate from a single and mostly uniform population of varying
repeaters. Within this population, the luminosity function cannot be steep, and
there must be minor differences in physical or behaviour parameters that
correlate with repeat rate.
