The problem of determining the neutron and count distributions in a multiplying assembly has been independently solved by many authors over the past 30 years. In all cases, the quadratic approximation is used for the probability generating function of the neutrons emitted per fission. In the present paper, this approximation is interpreted as one that almost exactly accounts for the fluctuations of two small samples, one of which is withdrawn from the totality of the neutrons existing at a given time, while the second is taken from all those that have been absorbed up to that time. The observed counts constitute the sample taken from the absorbed neutron population, while the usual distribution of the whole neutron population is obtained from that of the sampled neutrons by performing a suitable change of variable. According to this interpretation, the neutron distribution so obtained may contain rather large errors, and the only case for which we can say that the approximation is safe is that of the count distribution, provided the detector efficiency is kept very small. Indeed, numerical examples show that the relative errors in most cases are of one or two orders of magnitude larger for the neutron distribution than those for the count distribution.