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The 85 pages that link to Random variable, each with the reason it gives.

• Expected valueNarrower topic: Expectation averages the values assigned by this function, weighted by their probabilities.

• Probability distributionNarrower topic: A distribution describes the probabilities associated with a random variable’s possible values.

• Information theoryNarrower topic: Information theory describes sources and channels through probability distributions over outcomes.

• VarianceNarrower topic: Variance describes the distribution of values assigned by a random variable.

• Probability density functionNarrower topic: A density describes the distribution of a real-valued random variable.

• Sampling distributionNarrower topic: Before data are observed, a statistic computed from a random sample is itself a random variable.

• Stochastic processNarrower topic: Each indexed quantity in a stochastic process is a random variable.

• Normal distributionNarrower topic: A normal distribution describes the probability behavior of a continuous random variable.

• Binomial distributionNarrower topic: The binomial variable records the number of successes.

• Central limit theoremNarrower topic: The theorem applies to sequences of random variables, not directly to arbitrary datasets.

• Characteristic functionNarrower topic: The distribution encoded by a characteristic function belongs to a random variable.

• Law of large numbersNarrower topic: Repeated observations are modeled as random variables whose averages can be studied.

• Likelihood functionNarrower topic: The data are modeled as outcomes of random variables before their observed values are fixed.

• Linear regressionNarrower topic: Regression treats responses and often errors as random quantities.

• Analysis of varianceNarrower topic: ANOVA models observations as random outcomes around systematic effects.

• CorrelationNarrower topic: Correlation summarizes how two variables vary jointly across observations.

• Shannon entropyNarrower topic: The outcomes whose probabilities are averaged are represented by random variables.

• Cumulative distribution functionNarrower topic: The CDF describes the distribution of a random variable’s values.

• Regression analysisNarrower topic: Regression treats outcomes and often errors as random quantities.

• Statistical modelNarrower topic: Statistical models describe uncertain observations through random variables.

• Conditional expectationNarrower topic: The quantity being averaged conditionally is itself a random variable.

• Uncertainty quantificationNarrower topic: It provides the basic representation of uncertain quantities.

• CovarianceNarrower topic: Covariance summarizes how a pair of random variables behave together.

• Independent and identically distributed random variablesNarrower topic: Each member of an i.i.d. collection is a random variable.

• Probability mass functionNarrower topic: The mass function describes the probabilities associated with its possible values.

• Almost sure convergenceNarrower topic: Each term in the sequence assigns a value to every outcome.

• Moment-generating functionNarrower topic: The exponential inside the defining expectation is applied to a random variable.

• Convergence in probabilityNarrower topic: The sequence consists of random variables, whose deviations from the limit are measured probabilistically.

• Gaussian processNarrower topic: A Gaussian process assigns random variables to function values at individual inputs.

• Geometric distributionNarrower topic: The waiting time is a random variable whose possible values depend on the chosen convention.

• Strong law of large numbersNarrower topic: The theorem applies to sequences of random variables and their averages.

• Bernoulli distributionNarrower topic: The Bernoulli distribution describes the values of a random variable with two possible outcomes.

• Bernoulli trialNarrower topic: Coding success as one and failure as zero turns a trial into a random variable.

• Pseudorandom number generatorNarrower topic: Generators commonly encode samples intended to behave like draws from specified random variables.

• Correlation functionNarrower topic: Field values are treated as random variables when their statistical dependence is measured.

• Independent random variablesNarrower topic: Independence describes relationships among the distributions of random variables.

• Hypergeometric distributionNarrower topic: The number of sampled successes is the random quantity whose distribution is modeled.

• Concentration inequalityNarrower topic: The quantity whose unusually large deviations an inequality bounds.

• Linearity of expectationNarrower topic: The rule combines expectations of random variables, which need not be independent.

• Continuous mapping theoremNarrower topic: The theorem transforms random variables and studies the limits of their distributions.

• Random vectorNarrower topic: A random vector generalizes a scalar random variable to multiple coordinates.

• Slutsky's theoremNarrower topic: The theorem concerns sequences of these objects and their limiting distributions.

• Law of total expectationNarrower topic: The identity concerns the average of a random variable over its possible outcomes.

• Law of total varianceNarrower topic: The identity applies to a random variable with finite second moment.

• Kolmogorov's zero–one lawNarrower topic: The law starts with a sequence of these measurable functions.

• Skorokhod representation theoremNarrower topic: The conclusion realizes each measure as the law of a random variable.

• 68–95–99.7 ruleNarrower topic: The rule describes probabilities for values of a random variable with a normal distribution.

• Bienaymé's identityNarrower topic: Bienaymé's identity applies to sums of random variables.

• Correlation function measurementNarrower topic: Correlation functions describe dependence among random variables indexed across observations or positions.

• Cramér's decomposition theoremNarrower topic: The theorem concerns sums of random variables rather than arbitrary numerical decompositions.