The behaviors of electromagnetic (EM) propagation between two communication volumes can be described by a rank-2 dyadic angular spectrum. The present work investigates the characteristics of this spectrum in a random environment through Monte Carlo simulations. A variety of statistical properties are assessed. The results presented pay extra attention to the polarization change as plane wave components depart the transmit volume, interact with the scattering media, and arrive at the receive volume. It is observed that, largely in agreement with the common assumption, a transmit plane wave component can be converted to the two polarizations of plane waves in various receive directions with very low correlation and statistical bias in the presence of sufficient random scattering.