[en] This paper demonstrates use of the Hurwitz iterated fission probability method of estimating the neutron importance function for calculating the prompt neutron lifetime, the effective delayed neutron fraction and the first-order derivatives (or sensitivities) of the effective multiplication factor with respect to neutron constants and material densities. Special techniques of calculating aforementioned quantities have been proposed by different authors. This paper is based on these earlier works but presents all techniques from one point of view. It is noted that in all cases random contributions of adjoint-weighted values expressed through the integral importance of fission neutrons depending on the space variable only (rather than the differential neutron importance depending on the space, energy and angular variables) can be found. This importance is estimated by sampling auxiliary neutron histories. This approach can be implemented in Monte Carlo criticality codes without considerable modifications of calculation procedure. At the same time, it gives quite robust estimates of the adjoint-weighted quantities. While it has been used in multigroup Monte Carlo codes, it can be implemented in continuous-energy Monte Carlo codes without any visible difficulties. The approach is one of possible Monte Carlo interpretations of the Hurwitz iterated fission probability method while there are others. A comparative analysis of different interpretations is not done in this paper. (authors)