On the relation between the mass-ratio distribution in binary stars and the mass function for single stars.

The relationship between the mass-ratio distribution and the mass function is derived and the way in which use of a Salpeter mass function has led to confusion is shown. The expected distributions for spectroscopic binaries, both single- and double-lined, are also considered, and some of the diversity of previous results are explained, while assuming independence. It is concluded that unknown selection effects severely limit the information that can be extracted from these samples. Complete samples that avoid selection effects can be found and used to identify the finer details of the mass-ratio distribution.