The mean and variance of the number of matches let sill be, Basic Statistics

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The mean and variance of the number of matches let sill be

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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Basic Statistics: The mean and variance of the number of matches let sill be

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Basic Statistics: The mean and variance of the number of matches let sill be

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