Expectation of Discrete Uniform Distribution

Theorem
Let $X$ be a discrete random variable with the discrete uniform distribution with parameter $n$.

Then the expectation of $X$ is given by:
 * $E \left({X}\right) = \dfrac {n+1} 2$

Proof
From the definition of expectation:
 * $\displaystyle E \left({X}\right) = \sum_{x \in \Omega_X} x \Pr \left({X = x}\right)$

Thus: