We have studied the statistics of the output pulse width and effective broadening of the pulses which are affected by Polarization Mode Dispersion (PMD) of optical fiber. In this work, first we simulated numerically the optical fiber PMD. After the model examination according to the known characteristics and criterion for PMD, we have computed and shown the effect of the optical fiber PMD on the pulse shape. We have used the Monte Carlo method to investigate the dependence of the average output pulse width and effective broadening on the average Differential Group Delay (DGD) for Gaussian and super-Gaussian pulses (which are representative of RZ and NRZ data formats, respectively). It is shown that the previous analytical result for RZ data format is valid for NRZ data format. Also, we have shown that the dependence of the average effective broadening on the bit format and input pulse width is faded as the average DGD diminishes.