This paper deals with the use of Monte Carlo experiments for investigating noise phenomena associated with hot carrier transport in semiconductors. In the first part of the paper procedures and problems associated with the design and interpretation of such experiments are discussed. The use of a Monte Carlo experiment is then demonstrated by estimating the velocity fluctuation spectrum of electrons in GaAs. Significant new results and insights are obtained. In particular, two new Spectral peaks are discovered and explained in terms of underlying physical processes, certain simple intuitive assumptions often made in noise theory are shown to be unjustified, and a criterion for the minimum flight time needed for estimates of "conventional" diffusion coefficients is obtained.