Probability distribution functions for the parameters defining the properties of the binary star populations. The black lines show the theoretical distributions while the colored histograms show the results of our sampling. Upper panels: period distribution for the two limits in mass-ratios, as indicated by the legend, assuming a constant minimum orbital distance a_min = 0.21 AU (left) or the taking into account the RLOF when computing a_min (right). The limits for each mass-ratio are plotted with vertical lines. Middle left panel: distributions adopted for the mass ratio (green: GS distribution from Duquennoy & Mayor 1991; salmon: uniform distribution). Middle right panel: distribution of inclinations. Lower left panel: eccentricity distribution; the differences between the uniform theoretical distribution and the one sampled are due to the dependence of e on the semi-minor axis and therefore, the orbital period, as explained in the main text. Lower right panel: distribution of the argument of the periastron.