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Conditional expectation
Expected value of a random variable given that certain conditions are known to occur
Conditional expectation
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 this probability space. Depending on the context, the conditional expectation can be either a random variable or a function. The random variable is denoted E ( X ∣ Y ) {\displaystyle E(X\mid Y)} analogously to conditional probability. The function form is either denoted E ( X ∣ Y = y ) {\displaystyle E(X\mid Y=y)} or a separate...
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