The purpose of this paper is to develop a generalized formalism with which both the inherent neutron fluctuations in a steady system (the so–called zero power noise) and the neutron fluctuations induced by the fluctuation of the host material (power reactor noise or structural noise) can be treated simultaneously. To achieve this goal, a generalized form of the Rossi–alpha formula, i.e. the covariance function of neutron numbers, or detector counts, with a time delay τ is derived analytically for a subcritical system while the medium is randomly fluctuating between two states. The formalism used is backward–type master equations for the neutron probability distribution. The Rossi–alpha formula is suitable for calculating the auto–power spectral density of the neutron noise, and thus to make comparisons with power reactor noise calculations. The results obtained in this paper contain both the inherent fluctuations and the power reactor noise simultaneously, and reproduce either of these two separately in the corresponding limits.