A convolution is just a posh way of saying the distribution of a sum of independent random variables. So for a convolution of \(S = X_1 + X_2)\) where they take the values 0, 1, 2, 3, .... the probability of S being 2 is given by: \(P(S = 2) = P(X_1 = 0)P(X_2 = 2) + P(X_1 = 1)P(X_2 = 1) + P(X_1 = 2)P(X_2 = 0)\) What we have here is \(S = X_1 + X_2 + ... + X_n)\) and so we could work out the probabilities for S in a similar (but very painful) way. On a piece of paper this isn't going to happen for more than 2 variables. But a computer could do this.
