  We examine the role of the initial density and velocity distribution in the
gravitational collapse of a spherical inhomogeneous dust cloud. Such a collapse
is described by the Tolman-Bondi metric which has two free functions: the
`mass-function' and the `energy function', which are determined by the initial
density and velocity profile of the cloud. The collapse can end in a black-hole
or a naked singularity, depending on the initial parameters characterizing
these profiles. In the marginally bound case, we find that the collapse ends in
a naked singularity if the leading non-vanishing derivative of the density at
the center is either the first one or the second one. If the first two
derivatives are zero, and the third derivative non-zero, the singularity could
either be naked or covered, depending on a quantity determined by the third
derivative and the central density. If the first three derivatives are zero,
the collapse ends in a black hole. In particular, the classic result of
Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole,
is recovered as a special case. Analogous results are found when the cloud is
not marginally bound, and also for the case of a cloud starting from rest. We
also show how the strength of the naked singularity depends on the density and
velocity distribution. Our analysis generalizes and simplifies the earlier work
of Christodoulou and Newman [4,5] by dropping the assumption of evenness of
density functions. It turns out that relaxing this assumption allows for a
smooth transition from the naked singularity phase to the black-hole phase, and
also allows for the occurrence of strong curvature naked singularities.
