The aim of this note is to give an elegant proof of a result due to E. G. Olds which concerns the density distribution of the sum of independent uniform random variables non-identically distributed. The proof uses both analytical and combinatorial properties of Dirac distributions and their convolutions. The method is new and can apply to other situations.
"Dirac distributions related to sums of independent nonidentically uniform random variables." Braz. J. Probab. Stat. 35 (3) 435 - 441, August 2021. https://doi.org/10.1214/20-BJPS484