In this paper transient electromagnetic wave propagation in an inhomogeneous, cold plasma is considered. It is assumed that a constant magnetic induction is present and that the plasma is spatially inhomogeneous in the direction of the magnetic induction. Losses in the plasma are modeled with a collision frequency ν. The direct problem, which is to calculate the reflected and transmitted responses of the plasma, is considered in this paper. Special attention is paid to the precursor effects in the plasma and several examples of precursor effects in an inhomogeneous plasma are showed.