Herman Rubin wrote:
>
> If the distributions are on {0, 1, ..., k}, direct
> convolutions can get the results in O(nk^2) computations.

For direct convolutions, it is important to know whether you are
dealing with the case where the distributions of the Yi are the same,
or not. If they are the same and n is large, considerable savings can
be made by skipping some of steps and evaluating only:
(sum of 2), (sum of 4), (sum of 8), (sum of 16) etc.. You should also
consider whether you want the whole of the distribution or just the
tail(s), as this may affect how you chose to approach the problem.



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