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sample space
In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible outcomes are listed as elements in the set. It is common to refer to a sample space by the labels ''S'', Ω, or ''U'' (for "universal set").
For example, if the experiment is tossing a coin, the sample space is typically the set . For tossing two coins, the corresponding sample space would be . For tossing a single six-sided die, the typical sample space is (in which the result of interest is the number of pips facing up).
A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).
==Multiple sample spaces==
For many experiments, there may be more than one plausible sample space available, depending on what result is of interest to the experimenter. For example, when drawing a card from a standard deck of fifty-two playing cards, one possibility for the sample space could be the various ranks (Ace through King), while another could be the suits (clubs, diamonds, hearts, or spades).〔 A more complete description of outcomes, however, could specify both the denomination and the suit, and a sample space describing each individual card can be constructed as the Cartesian product of the two sample spaces noted above (this space would contain fifty-two equally likely outcomes). Still other sample spaces are possible, such as if some cards have been flipped when shuffling.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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