The probability distribution that a biopolymer has n ligands bound to it can be determined from the ligand-binding curve that gives the average number of ligands bound as a function of free-ligand concentration in solution. One fits the binding curve as a function of ligand concentration locally to an expansion in the ligand concentration. The expansion coefficients can be turned into moments of the ligand-binding distribution function which, using the maximum-entropy method, gives an accurate construction of the entire ligand-binding distribution function. A linear expansion gives two moments of the distribution while a cubic expansion gives four. In many cases two moments are sufficient to give a very accurate distribution function. The method is exactly analogous to the use of heat capacity data as a function of temperature to construct the enthalpy probability distribution. As with the case of the enthalpy distribution applied to proteins, knowledge of four moments of the distribution function is sufficient to resolve bimodal behavior in the distribution function. Several examples using model systems that involve independent units, cooperative units, and ligand-induced conformational changes (illustrating bimodal behavior) are given. We then examine literature data for the titration of ribonuclease and, using our method of moments, resolve all 30 average proton binding constants for the molecule.