Editing Conditional expectation (section)

{{short description|Expected value of a random variable given that certain conditions are known to occur}}
{{More footnotes needed|date=September 2020}}

In [[probability theory]], the '''conditional expectation''', '''conditional expected value''', or '''conditional mean''' of a [[random variable]] is its [[expected value]] evaluated with respect to the [[conditional probability distribution]]. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete [[probability space]], the "conditions" are a [[partition of a set|partition]] of this probability space.

Depending on the context, the conditional expectation can be either a random variable or a function. The random variable is denoted <math>E(X\mid Y)</math> analogously to [[conditional probability]]. The function form is either denoted <math>E(X\mid Y=y)</math> or a separate function symbol such as <math>f(y)</math> is introduced with the meaning <math>E(X\mid Y) = f(Y)</math>.