what is the sample space
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range of values of a randam variable is the definition of sample space
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In probability theory, the sample space[nb 1] 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 ordered 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 {head, tail}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}, commonly written {HH, HT, TH, TT}. If the sample space is unordered, it becomes {{head,head}, {head,tail}, {tail,tail}}.
For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).[5]
A well-defined sample space is one of three basic elements in a probabilistic model (aprobability 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).
For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}, commonly written {HH, HT, TH, TT}. If the sample space is unordered, it becomes {{head,head}, {head,tail}, {tail,tail}}.
For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).[5]
A well-defined sample space is one of three basic elements in a probabilistic model (aprobability 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).
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