Roundoff error for floating point representation of real data

In the present paper we define aprobabilistic model for the study ofthe relative roundoff error in the floating point representation ofreal data. In particular, starting from the assumption that real data is uniformly distributed in the interval (0,1), each floating point is assigned aprobability value corresponding to the proportion of real data assigned this floating point value. For each real number x～ U(0,1), we compute the relative roundoff error in the floating point representation and we calculate i t s expected value and variance.