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{{Probability fundamentals}}
In probability and statistics, a '''random variable''', '''random quantity''', '''aleatory variable''', or '''stochastic variable''' is basically a mapping from set of outcomes of a random experiment to real numbers. The name 'Random Variable' is misnomer. It is neither random, nor a variable. It is a special kind of function which takes input as set of outcomes of a random experiment, and gives a real number as output, which suppose to quantify the outcomes in some meaningful way. For example, say, the weather is a random experiment of the nature, and let's say, T is a function which predicts (maps) temperature from some measurable features of the weather, then we can say T is a random variable. The formal mathematical treatment of random variables is a topic in [[probability theory]]. In that context, a random variable is understood as a [[measurable function]] defined on a [[probability space]] that maps from the [[sample space]] to the real numbers.<ref name="UCSB">{{cite web | title = Economics 245A – Introduction to Measure Theory | url = http://econ.ucsb.edu/~doug/245a/Lectures/Measure%20Theory.pdf | last = Steigerwald | first = Douglas G. | publisher = University of California, Santa Barbara | accessdate = April 26, 2013}}</ref>
[[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.]]
A random variable's possible values might represent the possible outcomes of a yet-to-be-performed experiment, or the possible outcomes of a past experiment whose already-existing value is uncertain (for example, because of imprecise measurements or [[quantum uncertainty]]). They may also conceptually represent either the results of an "objectively" random process (such as rolling a die) or the "subjective" randomness that results from incomplete knowledge of a quantity. The meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself, but is instead related to philosophical arguments over the [[interpretation of probability]]. The mathematics works the same regardless of the particular interpretation in use.
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