  We study the distribution of dark matter in dwarf spheroidal galaxies by
modelling the moments of their line-of-sight velocity distributions. We discuss
different dark matter density profiles, both cuspy and possessing flat density
cores. The predictions are made in the framework of standard dynamical theory
of two-component (stars and dark matter) spherical systems with different
velocity distributions. We compare the predicted velocity dispersion profiles
to observations in the case of Fornax and Draco dwarfs. For isotropic models
the dark haloes with cores are found to fit the data better than those with
cusps. Anisotropic models are studied by fitting two parameters, dark mass and
velocity anisotropy, to the data. In this case all profiles yield good fits but
the steeper the cusp of the profile, the more tangential is the velocity
distribution required to fit the data. To resolve this well-known degeneracy of
density profile versus velocity anisotropy we obtain predictions for the
kurtosis of the line-of-sight velocity distribution for models found to provide
best fits to the velocity dispersion profiles. It turns out that profiles with
cores typically yield higher values of kurtosis which decrease more steeply
with distance than the cuspy profiles, which will allow to discriminate between
the profiles once the kurtosis measurements become available. We also show that
with present quality of the data the alternative explanation of velocity
dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.
