Domain of Variable/Examples/Points on Pair of Dice

Example of Domain of Variable
Let $S$ be the total number of points that are obtained when tossing a pair of dice.

The domain of $S$ is the set $\set {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}$.

$S$ is a discrete variable.

Proof
The set of points that can be obtained on a single die is $\set {1, 2, 3, 4, 5, 6}$.

Hence the set of points that can be obtained on a pair of die is found by adding each of the elements of $\set {1, 2, 3, 4, 5, 6}$ with each of the elements of the same set.