Countable Sample Space

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

• AKA: Discrete Sample Space.
• Context:
  • It can be:
    • a Categorical Sample Space (Unordered Discrete Sample Space).
    • a Nominal Sample Space (Ordered Discrete Sample Space).
  • It can be a Finite Sample Space.
  • …
• Example(s):
  • any Finite Sample Space, such as:
    • {Heads,Tails}, the Sample Space of a Coin Toss Experiment.
    • {1,2,3,4,5,6}, the Sample Space of a Dice Roll Experiment.
  • the Sample Space for the Coin Toss Experiment where the Coin is tossed until a Heads shows up (because the coin could be tossed indefinitely).
  • …
• Counter-Example(s):
  • The Time Duration [0, ∞) of a Lifetime Experiment, such as how long a Lightbulb will last.
  • The Scale of person Heights.
• See: Continuous Sample Space.

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References

2009

• http://www.statistics.com/resources/glossary/c/countnspc.php
  • Countable Sample Space: If a sample space contains finite or countably infinite number of sample points then such a sample space is referred to as a countable sample space.

2008

• (Qian) => Gang Qian. (2008). Basic Probability Theory." Lecture Notes: AME 598 Sensor Fusion, Arizona State University, Fall 2008.
  • Sample Space (S): defined as the set of all possible outcomes from a random experiment.
  • Countable or discrete sample space, one-to-one correspondence between outcomes and integers
  • Uncountable or continuous sample space

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