The mean and variance of the number of matches. Let Sill be the number of matches obtained by distributing, 1 to an urn, M balls, numbered 1 to M, among M urns, numbered 1 to M. It was shown in theoretical exercise 3.3 of Chapter 5 that E[SM] = 1 and Var [SM] = 1. Show this, using the fact that SM = X1 + ... + XM, in which Xk = 1 or 0, depending on whether the kth urn does or does not contain ball number k.