In the .author and van Eeden considered, as prior distributions for the cumulative, F, of the bio-assay problem, processes whose sample functions are, with probability one, distribution functions. The example we considered there had the undesirable property that its mean, E(F), was singular with respect to Lebesgue measure. In fact, Dubins and Freedman have shown that a class of such processes, which includes the example we considered, has sample functions F which are, with probability one, singular.