It is usually assumed that N samples of the time domain OFDM symbols have an identical Gaussian Probability Distribution (PD) in the real and imaginary parts. In this paper, we analyze the exact PD of M-QAM/OFDM symbols with N subcarriers. We show the general expression of the characteristic function of the time domain samples of M-QAM/OFDM symbols. As an example, theoretical discrete PD for both QPSK and 16-QAM cases is derived. The discrete nature of these distributions is used to reconstruct the distorted OFDM symbols due to deliberate clipping or amplification close to saturation. Simulation results show that the data reconstruction process can effectively lower the error floor level.