A rough, perfectly reflecting surface is first specified by the statistics of noise theory. If illuminated by a plane electromagnetic wave, such a surface would reflect statistically predictable fields. An attempt is made to formulate the problem of predicting the fields in terms of the statistics of the surface. The result is a series of integral expressions in which averages of the currents induced in the surface appear as unknown functions. Owing to mathematical complexities, these expressions are not solved for the average currents; however, a qualitative discussion is given of a known formula for the specular reflection coefficient of a gently rolling surface.