Conditional Expectation

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:

    The population of the world is a conditional population; these are not the best, but the best that could live in the existing state of soils, gases, animals, and morals: the best that could yet live; there shall be a better, please God.
    Ralph Waldo Emerson (1803–1882)

    A youthful mind is seldom totally free from ambition; to curb that, is the first step to contentment, since to diminish expectation is to increase enjoyment.
    Frances Burney (1752–1840)