  In this paper, we discuss the angular momentum distribution in the ground
states of many-body systems interacting via a two-body random ensemble.
Beginning with a few simple examples, a simple approach to predict P(I)'s,
angular momenta I ground state (g.s.) probabilities, of a few solvable cases,
such as fermions in a small single-j shell and d boson systems, is given. This
method is generalized to predict P(I)'s of more complicated cases, such as even
or odd number of fermions in a large single-j shell or a many-j shell, d-boson,
sd-boson or sdg-boson systems, etc. By this method we are able to tell which
interactions are essential to produce a sizable P(I) in a many-body system. The
g.s. probability of maximum angular momentum $I_{max}$ is discussed. An
argument on the microscopic foundation of our approach, and certain matrix
elements which are useful to understand the observed regularities, are also
given or addressed in detail. The low seniority chain of 0 g.s. by using the
same set of two-body interactions is confirmed but it is noted that
contribution to the total 0 g.s. probability beyond this chain may be more
important for even fermions in a single-j shell. Preliminary results by taking
a displaced two-body random ensemble are presented for the I g.s.
probabilities.
