Part II extends the work of Part I on probability distribution of power during a low source re-actor startup, by using a mathematical model in which the assumption of zero neutron lifetime is no longer made. This permits calculations to be carried to and beyond prompt critical, and consequently permits consideration of faster reactivity insertion rates than could be handled by the methods of Part I. A computational technique for the finite lifetime model is described. Numerical results are given, which extend the results of Part I.