The mean and variance of the number of matches let sill be, Ask an Expert

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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[S_M] = 1 and Var [S_M] = 1. Show this, using the fact that S_M = X₁ + ... + X_M, in which X_k = 1 or 0, depending on whether the kth urn does or does not contain ball number k.

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