In probability theory, a conditional expectation (also known as conditional expected value or conditional mean) is the expected value of a real random variable with respect to a conditional probability distribution.
The concept of conditional expectation is extremely important in Kolmogorov's measure-theoretic definition of probability theory. In fact, the concept of conditional probability itself is actually defined in terms of conditional expectation.
Read more about Conditional Expectation: Introduction, Formal Definition, Definition of Conditional Probability, Conditioning As Factorization, Conditioning Relative To A Subalgebra, Basic Properties
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