In Part I, statistical fluctuations of neutron populations in reactors are analyzed by means of an appropriate theoretical model which assumes zero neutron lifetime and one group of delayed neutrons. A computational technique is developed which employs the method of characteristics to calculate probability generating functions, thereby making possible the computation of the probability distribution of power during startup of a reactor with low source. Extensive numerical results are given for such computations for a wide range of source strengths and ramp reactivity insertion rates. The special relationships of fluctuations to safety considerations are discussed. Finally, the predictions of the model are compared with Godiva weak source transient data, and empirical criteria for conservative normalization of the model are presented.