  Observations of distant galaxies play a key role in improving our
understanding of the Epoch of Reionization (EoR). The observed Ly-alpha
emission line strength - quantified by its restframe equivalent width (EW) -
provides a valuable diagnostic of stellar populations and dust in galaxies
during and after the EoR. In this paper we quantify the effects of star
formation stochasticity on the predicted Ly-alpha EW in dwarf galaxies, using
the publicly available code SLUG ('Stochastically Light Up Galaxies'). We
compute the number of hydrogen ionizing photons, as well as flux in the Far UV
for a set of models with star formation rates (SFR) in the range 10-3-1
Msol/yr. From these fluxes we compute the luminosity, L-alpha, and the EW of
the Ly-alpha line. We find that stochasticity alone induces a broad
distribution in L-alpha and EW at a fixed SFR, and that the widths of these
distributions decrease with increasing SFR. We parameterize the EW probability
density function (PDF) as an SFR-dependent double power law. We find that it is
possible to have EW as low as ~EW0/4 and as high as ~3 times the EW0, where EW0
denotes the expected EW in the absence of stochasticity. We argue that
stochasticity may therefore be important when linking drop-out and narrow-band
selected galaxies, when identifying population III galaxies, and that it may
help to explain the large EW (EW > 100 - 200 A) observed for a fraction of
Ly-alpha- selected galaxies. Finally, we show that stochasticity can also
affect the inferred escape fraction of ionizing photons from galaxies. In
particular, we argue that stochasticity may simultaneously explain the observed
anomalous ratios of the Lyman continuum flux density to the (non-ionizing) UV
continuum density in so-called Lyman-Bump galaxies at z = 3.1, as well as the
absence of such objects among a sample of z = 1.3 drop-out galaxies.
