Discrete Uniform Distribution

$X \sim Uniform ({1, 2, \dots, m})$

A random variable is uniformly distributed if the probability of each $x \in S$ is equal. For the probabilities to be equal and add up to one, and since there are $m$ of $x \in S$ , $p_{X} (x_{i}) = \frac{1}{m}$
$p_{X} (x) = \frac{1}{m}, x \in {1, 2, \dots, m}$
$F_{X} (x) =$
$M_{X} (t) =$
$E [X] = \frac{m + 1}{2}$
$var (X) = \frac{m ^{2} - 1}{12}$
An example of a random variable would be $X =$ the number of pips on a die face after a roll. There are 6 outcomes because $m = ∣ {1, 2, 3, 4, 5, 6} ∣ = 6$ , meaning $p_{X} (x_{i}) = \frac{1}{m} = \frac{1}{6}$