  Gravitational-wave observations of inspiralling binary neutron star systems
can be used to measure the neutron-star equation of state (EOS) through the
tidally induced shift in the waveform phase that depends on the tidal
deformability parameter $\lambda$. Previous work has shown that $\lambda$, a
function of the neutron-star EOS and mass, is measurable by Advanced LIGO for a
single event when including tidal information up to the merger frequency. In
this work, we describe a method for stacking measurements of $\lambda$ from
multiple inspiral events to measure the EOS. We use Markov chain Monte Carlo
simulations to estimate the parameters of a 4-parameter piecewise polytrope EOS
that matches theoretical EOS models to a few percent. We find that, for
"realistic" event rates ($\sim 40$ binary neutron star inspiral events per year
with signal-to-noise ratio $> 8$ in a single Advanced LIGO detector), combining
a year of gravitational-wave data from a three-detector network with the
constraints from causality and recent high mass neutron-star measurements, the
EOS above nuclear density can be measured to better than a factor of two in
pressure in most cases. We also find that in the mass range
$1M_\odot$--$2M_\odot$, the neutron-star radius can be measured to better than
$\pm 1$ km and the tidal deformability can be measured to better than $\pm 1
\times 10^{36}$ g cm$^2$ s$^2$ (10%--50% depending on the EOS and mass). The
overwhelming majority of this information comes from the loudest $\sim 5$
events. Current uncertainties in the post-Newtonian waveform model, however,
lead to systematic errors in the EOS measurement that are as large as the
statistical errors, and more accurate waveform models are needed to minimize
this error.
