# 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.)?

• First of all, you haven't defined a distribution, but I'm assuming that you're picking the number uniformly and independently. Second, what do you mean by "estimate the distribution of Sum"? What kind of answer are you looking for? – Yuval Filmus May 11 '15 at 14:23