  We explore the use of a sufficient statistic based on the data of samples
that are selected under the M_0 capture-recapture closed population model
(Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based
on a sufficient statistic is then presented. Though the improvements made on
the preliminary capture-recapture estimates are likely to be negligible, this
body of work is primarily intended to contribute to the theory around the
capture-recapture models. The code for a simulation is provided in the
appendix.
