A random medium is considered, composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure, statistically homogeneous on all but molecular length scales. The equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed. Various particle-particle and particle-obstacle correlation functions, which differ from the corresponding functions for a fully equilibrated binary mixture, are defined through an averaging process over the static ensemble of obstacle configurations and application of topological reduction techniques. The Ornstein-Zernike equations also differ from their equilibrium counterparts.