Estimate distribution of a composite variable Suppose I have N sets of numbers (10 numbers per set) {a1, ....., a10}. I form a sum by taking one number at random from each set. SUM = num from set 1 +......+ num from set N. If I do this a large number of times I will generate a large number of different values for the SUM variable. How can I estimate the distribution of the SUM values (P10, P50, P90 etc.)?
Use a convolution.

For instance, write the generating function for each set, then multiply the generating functions; this gives you the generating function for the distribution of the sum.

This gives you the exact distribution (which is even better than an approximation!).