Transit times (the times for individual particles to traverse the distance between two fixed heights) have been widely used to estimate the mean of the instantaneous velocity. Individual particles in a dilute dispersion have velocities that are approximately normally distributed. Also, the velocity of any particle varies continuously, but erratically, with time. These features, which complicate the analysis of transit times, are accurately described by the three-parameter Markov model. We have applied a fourth-order stochastic Runge-Kutta method to the differential equations for this model to obtain position and velocity at discrete times. Crossing times and velocities are determined by interpolation. We have used simulations to clarify the concepts of crossing velocities, first-crossing velocities, ’calming sections’, and transit times. Means calculated from total distance/total time agree closely with the mean chosen for the simulation. This agreement, which persists far beyond any variability yet encountered in experimental work, validates the use of transit times to estimate mean velocity.