Roundoff error statistics for a continuous range of multiplier coefficients

A general statistical analysis is presented for the roundoff error that is generated when a discrete random multiplicand, taking on only integer values, is multiplied by a real coefficient and the result rounded back to the nearest integer. Numerical results are provided for mean, variance, correlation with multiplicand, and correlation between roundoff errors, as functions of multiplier coefficient value, variance of multiplicand, and correlation of multiplicands.