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For an integrable random variable and a sub--algebra, the almost-surely unique measurable random variable whose integral over every event in that sub--algebra agrees with the original variable's integral.
durrett-probabilityEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
At each stage of a filtration, conditional expectation projects an integrable random variable onto the information represented by the corresponding sub--algebra.
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.
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-probabilityEach relation below starts at this concept.
No direct relations are authored in this direction.