Theorem 6.4.2. Properties of the Hypergeometric Distribution.

  1. \(f(x) = \frac{\binom{n_1}{x} \binom{n-n_1}{r-x}}{\binom{n}{r}}\) satisfies the properties of a probability function.
  2. \(\displaystyle \mu = r \frac{n_1}{n}\)
  3. \(\displaystyle \sigma^2 = r \frac{n_1}{n} \frac{n_2}{n} \frac{n-r}{n-1}\)
  4. \(\displaystyle \gamma_1 = \frac{(n - 2 n_1)\sqrt{n-1}(n - 2r)}{r n_1 (n - n_1) \sqrt{n-r}(n-2)}\)
  5. \(\gamma_2 = \) very complicated!

Proof.

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