Dice Roll Experiment

A dice roll experiment is an multinomial random experiment with [math]\displaystyle{ k=6 }[/math] composed of dice throw events.

• AKA: Dice Throw Process, 6-Sided Dice Toss Experiment.
• Context:
  • It can involve:
    • a Unbiased Dice/Fair Dice.
    • an Biased Dice/Unfair Dice.
  • It can be associated with a Dice Roll Trial (e.g. {(1,5),(4,5),(5,4),(2,2)}
  • It can be represented by a Categorical Random Variable.
  • …
• Example(s):
  • a One-Dice Roll Experiment (Roll a dice one time), with:
    • Sample Space={1,2,3,4,5,6} with 6x1=6 Outcomes.
    • Event Space={{},{1},{2},... {1,2} … {2,4,6} … {1,3,4,5} … {1,2,3,4,5,6}} with 2⁶=64 Events.
  • a Two-Dice Roll Experiment (Roll a dice two consecutive times), with:
    • Sample Space={(1,1),(1,2),...,(6,6)} with 6x6=36 Outcomes.
    • Event Space={{},{(1,1)},{(1,2)} … {(1,1),(3,5)} … } with 2⁴ Events.
  • …
• Counter-Example(s):
  • a Sequential Random Experiment, such as toss a coin two consecutive times, roll a dice two times, and draw one card from a card deck.
  • a Two-Sided Coin Toss Experiment.
  • a Card Draw Experiment.
• See: Craps Game Experiment.

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