Question: Consider the hypergeometric distribution with parameters r, n, and N. Suppose r depends on N in such as way that r/N p as N

Consider the hypergeometric distribution with parameters r, n, and N. Suppose r depends on N in such as way that r/N → p as N → ∞, where 0 < p < 1. Show that the mean and variance of the hypergeometric distribution converges to the mean and variance, respectively, of a binomial distribution with parameters n and p, as N → ∞.

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