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A note on the sum of uniform random variables

By Aniello Buonocore, Enrica Pirozzi and Luigia Caputo


An inductive procedure is used to obtain distributions and probability densities for the sum Sn of independent, non-equally uniform random variables. Some known results are then shown to follow immediately as special cases. Under the assumption of equally uniform random variables some new formulas are obtained for probabilities and means related to Sn. Finally, some new recursive formulas involving distributions are derived.

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