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A measurable function from a probability space to a measurable value space.
The probability space and value-space -algebra are part of the data. Traditionally the codomain is or ; for a general measurable codomain, “random element” is also common.
wp-random-variablenlab-random-variabledurrett-probabilityEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Identify the map domain with the probability space and retain the measurable codomain as the value space.
Feed several structures into a construction junction and impose compatibility between them.
wp-random-variabledurrett-probabilityEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Conditional expectation is another random variable determined from the original one and the conditioning information, not generally a pointwise average over outcomes.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
durrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
A real-valued random variable with finite absolute first moment has expectation .
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-expected-valuenlab-physics-expectation-valuedurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
Supply measurable random variables on one common probability space.
Feed several structures into a construction junction and impose compatibility between them.
wp-stochastic-processwp-random-variabledurrett-probabilityThis is an authored directed relation from the source endpoint to the target endpoint.
The law of is the pushforward measure on its measurable value space.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-probability-distributionnlab-probability-distributiondurrett-probability