Definitions for random variable
Random House Webster's College Dictionary
a statistical quantity that can take any of the values of a specified set in accordance with an associated probability distribution.
Ref: Also called variate.
Origin of random variable:
random variable, variate, variant, stochastic variable, chance variable(noun)
a variable quantity that is random
A quantity whose value is random and to which a probability distribution is assigned, such as the possible outcome of a roll of a dice.
A measurable function from a sample space to the measurable space of possible values of the variable.
In probability and statistics, a random variable or stochastic variable is a variable whose value is subject to variations due to chance. As opposed to other mathematical variables, a random variable conceptually does not have a single, fixed value; rather, it can take on a set of possible different values, each with an associated probability. 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. They may also conceptually represent either the results of an "objectively" random process, 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 instead related to philosophical arguments over the interpretation of probability. The mathematics works the same regardless of the particular interpretation in use. Random variables can be classified as either discrete or as continuous. The mathematical function describing the possible values of a random variable and their associated probabilities is known as a probability distribution. The realizations of a random variable, that is, the results of randomly choosing values according to the variable's probability distribution, are called random variates.
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