  The distribution of the sum of independent identically distributed uniform
random variables is well-known. However, it is sometimes necessary to analyze
data which have been drawn from different uniform distributions. By inverting
the characteristic function, we derive explicit formulae for the distribution
of the sum of n non-identically distributed uniform random variables in both
the continuous and the discrete case. The results, though involved, have a
certain elegance. As examples, we derive from our general formulae some special
cases which have appeared in the literature.
