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Using the population synthesis code StarTrack we construct the first synthetic X-ray binary populations for direct comparison with the X-ray luminosity function (XLF) of NGC 1569 observed with Chandra. Our main goal is to examine whether it is possible to reproduce the XLF shape with our models, given the current knowledge for the star-formation history of this starburst galaxy. We thus produce hybrid models meant to represent the two stellar populations: one old, metal-poor with continuous star-formation for 1.5 Gyr and another recent and metal-rich population. To examine the validity of the models we compare XLFs calculated for varying ages of the populations and varying relative weights for the star-formation rates in the two populations. We find that, for typical binary evolution parameters, it is indeed possible to quite closely match the observed XLF shape. The robust match is achieved for an age of the young population and a ratio of star formation rates in the two populations that are within factors of 1.5 and 2, respectively, of those inferred from HST observations of NGC 1569. In view of this encouraging first step, we discuss the implications of our X-ray binary models and their potential as tools to study binary populations in galaxies

X-Ray Binary Populations: The Luminosity Function of NGC 1569