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
Famous quotes containing the words conditional and/or expectation:
“Conditional love is love that is turned off and on....Some parents only show their love after a child has done something that pleases them. “I love you, honey, for cleaning your room!” Children who think they need to earn love become people pleasers, or perfectionists. Those who are raised on conditional love never really feel loved.”
—Louise Hart (20th century)
“For, the expectation of gratitude is mean, and is continually punished by the total insensibility of the obliged person. It is a great happiness to get off without injury and heart-burning, from one who has had the ill luck to be served by you. It is a very onerous business, this being served, and the debtor naturally wishes to give you a slap.”
—Ralph Waldo Emerson (1803–1882)