The methodology of Pál and Bell has been used to derive a master equation for the probability generating function, which governs the detector counting statistics in zero power reactors. The resulting formalism has led to rigorous derivations of the Feynman Y function and the covariance function, which include spatial and spectral corrections and which can be implemented in presently available neutron transport codes. As a by-product of the present formalism, a closure-problem-free derivation of the Boltzmann equation for neutron transport has been obtained.