  We have modeled the displacement of luminous X-ray binaries from star
clusters in star-burst galaxies with an evolutionary population synthesis code
developed by Hurley et al. (2000, 2002). In agreement with Kaaret et al.
(2004), we find significant spatial offset of X-ray sources from their parent
clusters, and the apparent X-ray luminosity vs. displacement correlation can be
roughly reconstructed. The correlation is not sensitive to the fundamental
properties of the clusters (e.g., initial mass functions of the binary stars)
and the kick velocity imparted to the newborn compact stars, except the common
envelope parameter. We present the distributions of the main parameters of the
current X-ray binaries, which may be used to constrain the models for the
formation and evolution of X-ray binaries with future optical observations.
