  We use recent neutrino dimuon production data combined with a global
deep-inelastic parton fit to construct a new parton set, NNPDF1.2, which
includes a determination of the strange and antistrange distributions of the
nucleon. The result is characterized by a faithful estimation of uncertainties
thanks to the use of the NNPDF methodology, and is free of model or theoretical
assumptions other than the use of NLO perturbative QCD and exact sum rules.
Better control of the uncertainties of the strange and antistrange parton
distributions allows us to reassess the determination of electroweak parameters
from the NuTeV dimuon data. We perform a direct determination of the |V_cd| and
|V_cs| CKM matrix elements, obtaining central values in agreement with the
current global CKM fit: specifically we find |V_cd|=0.244\pm 0.019 and
|V_cs|=0.96\pm 0.07. Our result for |V_cs| is more precise than any previous
direct determination. We also reassess the uncertainty on the NuTeV
determination of \sin^2\theta_W through the Paschos-Wolfenstein relation: we
find that the very large uncertainties in the strange valence momentum fraction
are sufficient to bring the NuTeV result into complete agreement with the
results from precision electroweak data.
