Constraining the Fast Radio Burst (FRB) properties using the detections
  at Parkes, ASKAP and CHIME
  We demonstrate how the FRB redshift and fluence distributions from the
Parkes, ASKAP and CHIME telescopes can be used together to constrain the
properties of the FRB population. Here we consider a simple model where all the
FRBs have the same spectral index $\alpha$ and rest frame energy $E$ (specified
in a fixed band $2128\;{\rm MHz}$ to $2848\;{\rm MHz}$). We find that the
constraints on $(\alpha,E)$ depend on the scattering model for pulse broadening
in the inter-galactic medium. For no scattering we find that there is a region
of parameter space where the predictions are simultaneously consistent with the
FRB redshift and fluence distributions at all three telescopes. The allowed
$\alpha$ range is bounded by $-6.0\leq \alpha \leq-3.6$ and the allowed $E$
range is bounded by $1.79\times 10^{33}{\rm J} \leq E \leq 5.41\times
10^{33}{\rm J}$. Our analysis also rules out an empirical scattering model
where the FRB pulse broadening in the IGM is predicted by extrapolating pulse
broadening observed for pulsars in the ISM.
