  For the Gaussian and Laguerre random matrix ensembles, the probability
density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - <x>)$
is computed exactly and shown to satisfy a central limit theorem as $N \to
\infty$. For the circular random matrix ensemble the p.d.f.'s for the linear
statistics ${1 \over 2} \sum_{j=1}^N (\theta_j - \pi)$ and $- \sum_{j=1}^N \log
2|\sin \theta_j/2|$ are calculated exactly by using a constant term identity
from the theory of the Selberg integral, and are also shown to satisfy a
central limit theorem as $N \to \infty$.
