The deposition of positrons from the passage of a positronium beam through a Tokamak plasma and the subsequent radial transport of positrons to the limiter are simulated. The signal created by the annihilation of positrons at the limiter is calculated for several different transport models. Loss processes, such as reformation of positronium and annihilation of positrons by plasma electrons, are examined to determine how they affect the annihilation signal. An analysis of how quantities relevant to electron-mass particle transport can be obtained from a positron transport experiment is included.