  The discovery of gravitational waves from compact objects coalescence opens a
brand-new window to observe the universe. With more events being detected in
the future, statistical examinations would be essential to better understand
the underlying astrophysical processes. In this work we investigate the
prospect of measuring the mass function of black holes that are merging with
the neutron stars. Applying Bayesian parameter estimation for hundreds of
simulated neutron star$-$black hole (NSBH) mergers, we find that the parameters
for most of the injected events can be well recovered. We also take a Bayesian
hierarchical model to reconstruct the population properties of the masses of
black holes, in the presence of a low mass gap, both the mass gap and power-law
index ($\alpha$) of black hole mass function can be well measured, thus we can
reveal where the $\alpha$ is different for binary black hole (BBH) and NSBH
systems. In the absence of a low mass gap, the gravitational wave data as well
as the electromagnetic data can be used to pin down the nature of the merger
event and then measure the mass of these very light black holes. However, as a
result of the misclassification of BBH into NSBH, the measurement of $\alpha$
is more challenging and further dedicated efforts are needed.
