Theorem 6.2.2. Properties of the Discrete Uniform Probability Function.

\(f(x) = \frac{1}{n}\) over \(R\) = {1, 2, 3, ..., n} satisfies the properties of a discrete probability function and
  1. \(\displaystyle \mu = \frac{1+n}{2}\)
  2. \(\displaystyle \sigma^2 = \frac{n^2-1}{12}\)
  3. \(\displaystyle \gamma_1 = 0\)
  4. \(\displaystyle \gamma_2 = 3 - \frac{6}{5}\frac{n^2+1}{n^2-1}\)
  5. Distribution function \(F(x) = \frac{x}{n}\) for \(x \in R\text{.}\)

Proof.

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