Domain of Variable/Examples/Points on Pair of Dice
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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.
$\blacksquare$
Sources
- 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Variables and Graphs: Solved Problems: Variables: $1.2 \ \text{(c)}$