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The entropy of an absolutely continuous distribution with probability density function is defined as . The formal maximization of , subject to the moment constraints , leads to , where the have to be chosen so as to satisfy the moment constraints. Only the case is considered. It is shown that when has finite range, a distribution maximizing the entropy exists and is unique. When the range is , the maximum-entropy distribution exists if, and only if, , and a table is given which enables the maximum-entropy distribution to be computed. The case is discussed in some detail.