show the prediction of the astrophysical  from binary black holes (BBH) and binary neutron stars (BNS), along with its statistical uncertainty due to Poisson uncertainties in the local binary merger rate. We plot the upper limit allowed from adding the background from neutron star-black hole (NSBH) binaries as a dotted line. We use the same binary formation and evolution scenario to compute the  from BBH and BNS as in [@gw170817_stoch], but we have updated the mass distributions and rates to be consistent with the most recent results given in [@gwtc-1; @RatesAndPop_O2]. For NSBHs, we use the same evolution with redshift as BNSs. As in [@gw170817], for BBH we include inspiral, merger and ringdown contributions computed in [@AjithEA_2008], while for NSBH and BNS we use only the inspiral part of the waveform. For the BBH mass distribution, we assume a power law in the primary mass $p(m_1)\propto m_1^{-2.3}$ with the secondary mass drawn from a uniform distribution, subject to the constraints $5 M_\odot \leq m_2 \leq m_1 \leq 50 M_\odot$. In Ref. [@gwtc-1], rate estimates were computed by two pipelines, PyCBC [@pycbc-1] and GstLAL [@gstlal-1]. We use the merger rate measured by GstLAL, $R_{\rm local}=56^{+44}_{-27}{\rm Gpc^{-3} yr^{-1}}$ [@gwtc-1], because it gives 