  The W and Z boson production was measured via the muonic decay channel in
proton-lead collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV at the Large Hadron
Collider with the ALICE detector. The measurement covers backward ($-4.46 <
y_{\rm cms} < -2.96$) and forward ($2.03 < y_{\rm cms} < 3.53$) rapidity
regions, corresponding to Pb-going and p-going directions, respectively. The
Z-boson production cross section, with dimuon invariant mass of
$60<m_{\mu\mu}<120$ GeV/$c^2$ and muon transverse momentum ($p_{\rm T}^\mu$)
larger than 20 GeV/$c$, is measured. The production cross section and charge
asymmetry of muons from W-boson decays with $p_{\rm T}^\mu>10$ GeV/$c$ are
determined. The results are compared to theoretical calculations both with and
without including the nuclear modification of the parton distribution
functions. The W-boson production is also studied as a function of the
collision centrality: the cross section of muons from W-boson decays is found
to scale with the average number of binary nucleon-nucleon collisions within
uncertainties.
