An inductive procedure is used to obtain distributions and probability densities for the sum $S_n$ 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 $S_n$. Finally, some new recursive formulas involving distributions are derived.
A Note on the Sum of Uniform Random Variables
CAPUTO, LUIGIA
2009-01-01
Abstract
An inductive procedure is used to obtain distributions and probability densities for the sum $S_n$ 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 $S_n$. Finally, some new recursive formulas involving distributions are derived.
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