An analytical approach is presented to evaluate the impact of polarization mode dispersion on the average bit error rate (BER) performance of an intensity modulated direct detection (IM-DD) optical transmission system considering Maxwellian distribution for the differential group delay (DGD). The results show that the performance of an IM-DD system suffers power penalty of 0.27 dB, 0.45 dB and 2.4 dB corresponding to mean DGD of 20 ps, 35 ps and 40 ps respectively at a BER of 10 -9 operating at a bit rate of 10 Gb/s. Furthermore, at increased values of the mean DGD there occur BER floors above 10 -9 which can not be lowered by further increasing the signal power. It is noticed that BER floors occur at about 2x10 -9 , 10 -7 and 10 -5 corresponding to mean DGD of 45 ps, 50 ps and 60 ps respectively at 10Gb/s. The effect of PMD is found to be more detrimental at higher bit rates.