  We present an X-ray binary population synthesis model, and use it to simulate
the evolution of X-ray binaries formed in a burst of star formation of duration
20 Myr and star-formation rate 10 M_sun/yr. Our goal is to explain the hard
(2-10 keV) X-ray properties of populations of extragalactic X-ray binaries
recently observed by the Chandra X-Ray Observatory, especially those associated
with recent or ongoing episodes of vigorous star formation. Our simulated X-ray
binary population reaches a maximum 2-10 keV luminosity of ~4e40 erg/s after
approximately 20 Myr. The X-ray luminous phase is sustained for a period of
several hundreds of Myr by succeeding populations of systems with lighter
secondary stars, i.e., it persists long after the star-formation episode has
ended. These results are insensitive to the poorly-constrained values of the
initial mass function and the average mass ratio between accreting and donor
stars. The computed peak X-ray luminosity is consistent with
observationally-derived correlations between the star-formation rate and the
observed hard X-ray luminosity. Model cumulative luminosity functions at the
earliest times have power-law indices in agreement with those derived from
observations of actively star-forming galaxies. The model cumulative luminosity
functions become increasingly steeper with time as the most luminous systems
die off, which offers an explanation for the difference in the slopes of
observed cumulative luminosity functions of young and old stellar populations.
