Upper panel: black histogram shows the distribution of the logarithm of the reduced mass function, Y = f(m) /M₁, for the sample of spectroscopic binaries from M07, while the red dotted line connecting filled dots is our best model (see text). Lower panel: this shows the two components entering into our best-fit model using a Monte Carlo approach: The cyan dashed line connecting solid dots is the distribution that one would expect for a uniform mass-ratio distribution, while the blue dotted line connecting crosses corresponds to having 22% of systems with a Gaussian distribution of Y, centred around Y = 0.007 and a standard deviation of 0.0009. The best-fit red line in the upper panel is the sum of these two distributions.