The fluctuating populations of particles in a reactor are described in usual kinetics studies by the “numbers” of neutrons and precursors which, in the absence of feedback mechanisms, can be identified with first moments of the population distributions. At a higher level of description, variances and covariances of the neutron and precursor populations are determined from equations similar to the first-moment equations. The behavior of these first and second moments for time-varying reactors is explored here analytically and numerically, and inferences are made as to the effect of initial reactor conditions and modes of reactivity change on this dynamic behavior.