  Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric
matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix
entries are independent identically distributed random variables, with an
arbitrary probability distribution.
  These expectations are polynomials in the moments of the matrix entries ;
they provide useful information on the spectral density of the ensemble in the
large $n$ limit. They also are a straightforward tool to examine a variety of
rescalings of the entries in the large $n$ limit.
