The random medium model has been used quite successfully in the interpretation of active and passive microwave remote sensing data from earth terrain. In the random medium model, a correlation function with associated mean and variance is used to describe the random permittivity fluctuations. Most of the correlation functions used, thus far, in the random medium model have been of exponential form, or of other simple expressions derived from physical arguments. In this paper, we calculate the correlation function for a specific physical model of the random medium which is a random collection of discrete scatterers imbedded in a background medium of constant permittivity. Correlation functions are calculated for impenetrable and penetrable spherical scatterers. Once the correlation function is obtained, the strong fluctuation theory is used to calculate the effective permittivity. Then, the distorted Born approximation is used to calculate backscattering coefficients for a halfspace configuration. Theoretical results are illustrated by comparing effective permittivities and backscattering coefficients obtained from the penetrable and impenetrable models.