Discrete Uniform Distribution

Tags

math

For a discrete random variable \( X \) where \( X \) is defined over a set of distinct values that're all equally likely. I.E. \( P(X = x_i) = \frac{1}{n}, \; i = 1, 2, 3, \dots, n \)

An example of a discrete uniform distribution is the roll of a dice. There're 6 outcomes and each are equally likely.

From this we can define:

\begin{align} E(X) &= \frac{n+1}{2} \
Var(X) &= \frac{n^2 + 1}{12} \end{align}