Random variable: Difference between revisions

Revision as of 10:28, 25 April 2024

Revision as of 10:34, 25 April 2024

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* the [[Domain of a function|___domain]] is the set of possible [[Outcome (probability)|outcomes]] in a [[sample space]] (e.g. the set <math>\{H,T\}</math> which are the possible upper sides of a flipped coin heads <math>H</math> or tails <math>T</math> as the result from tossing a coin); and

* the [[Range of a function|range]] is a [[measurable space]] (e.g. corresponding to the ___domain above, the range might be the singleton set <math>\{0.5\}</math> if the function were to represent the typical probability of the outcomes, in which case both <math>H</math> and <math>T</math> would map to 0.5. Alternatively, it might also be completely arbitrary and be the set <math>\{-1, 1\}</math> if say heads <math>H</math> mapped to -1 and <math>T</math> mapped to 1). Typically, the range of a random variable is set of [[Real number|real numbers]].

[[File:Random Variable as a Function-en.svg|thumb|This graph shows how random variable is a function from all possible outcomes to real values. It also shows how random variable is used for defining probability mass functions.]]