This work characterizes the radio frequency (RF) power distribution within a given area via its mean and variance in three particular geometries. Through our statistical approach we have developed computationally simple equations that can be used to compute the mean value and variance of the RF power received in a circular area and in some other geometries without numerical evaluations of integrals and which improve on the results/methods provided in the literature to date. We begin our study with the analysis of the received power on a linear trajectory and then we extend the result for a circular geometry. We have validated our results via Monte Carlo simulations. These results are useful both the study of the coverage of a RF transmitter and to identify spectrum holes.