A mathematical method is described for the computation of the probability distribution of neutron populations in a point reactor with a weak source. The author and his colleagues have previously described a method for doing such computations, and G. I. Bell has described a different method; the present paper uses ideas from both of these older methods plus new formulations for computing the probability distribution from values of the generating function, for evaluating the probability distribution of precursor decay rates instead of that of neutron populations, and for evaluating the effect of short neutron lifetime without using unnecessarily short time steps in numerical integration. As a result, the method presented here is more widely applicable and more accurate than the older methods. The reactor model used here permits taking account of six delayed-neutron precursor groups and of finite neutron lifetime.