Categorical Sample Space

A Categorical Sample Space is a Sample Space that is a Categorical Set.

• AKA: Unordered Discrete Sample Space.
• Context:
  • It can be represented by a Categorical Random Variable.
  • It can be:
    • a Categorical Sample Space (Unordered Discrete Sample Space).
    • a Nominal Sample Space (Ordered Discrete Sample Space).
• Example(s):
  • Ω = {Heads, Tails}, the Sample Space associated with the Random Experiment of a Coin Toss Experiment.
  • Ω = {1,2,3,4,5,6}, the Sample Space associated with a Dice Roll Experiment, when the Event Space does not order the elements (e.g. Odd 1,3,5 vs. Even 2,4,6).
  • …
• Counter-Example(s):
  • Ω = {1,2,3,4,5,6}, the Sample Space associated with a Dice Roll Experiment, when the Event Space does order the elements (such as a Craps Game).
  • Ω = {(2,Spades), ..., (Ace,Diamonds)} , the Sample Space associated with a Card Draw Experiment.
• See: Ordinal Sample Space, Numerical Sample Space.

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