random variable

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random variable

A student rolls a die to illustrate a random variable.

Definition
  1. Noun:
    • A variable quantity that is random: A numerical quantity whose value depends on the outcomes of a random phenomenon or experiment. It is a function that assigns a real number to each possible outcome in a sample space.
Usage Examples
  • Noun:
    • The outcome of a coin flip can be modeled using a random variable. (Here, 'random variable' is the subject naming the mathematical concept used to represent the flip's result.)
    • We defined a random variable X to represent the sum of the two dice. (In this sentence, 'random variable' is the object being defined, specifying what 'X' is.)
    • The probability distribution describes the behavior of the random variable. (This example shows 'random variable' as the object of a preposition, indicating what the distribution describes.)
Advanced Usage
  • "to be a function of a random variable": Indicates that one quantity's value is determined by the outcome of another random process.
    • The profit is a function of the random variable representing market demand.
  • "independent and identically distributed (i.i.d.) random variables": A key concept in statistics referring to a sequence of random variables with the same probability distribution and mutual independence.
    • The theorem applies to a sequence of i.i.d. random variables.
Variants and Related Words
  • Stochastic variable (n): A synonym for random variable, often used in more formal or theoretical contexts.
  • Variate (n): Another less common synonym for random variable.
  • Random vector (n): A generalization of a random variable to multiple dimensions (i.e., a vector whose components are random variables).
Synonyms
  • Stochastic variable: A variable subject to randomness.
  • Chance variable: Emphasizes the dependence on chance.
Related Phrases and Concepts
  • Expected value of a random variable: The long-term average or mean value of the random variable.
    • Calculate the expected value of the random variable to find the average return.
  • Variance of a random variable: A measure of the dispersion or spread of the random variable's possible values.
    • A high variance indicates the random variable's outcomes are widely spread.
  • Realization of a random variable: The actual observed value that the random variable takes after an experiment is performed.
    • After rolling the die, the realization of the random variable was 4.
random variable

A student rolls a die to illustrate a random variable.

Noun
  1. a variable quantity that is random

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