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Realization
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Realization

In probability and statistics, a realization or observation (also called observed value) of a random variable or random element is the value that is actually observed or measured.1

In probability theory, a random variable is a function X defined from a sample space \Omega to the state space.

If an element in \Omega is mapped to an element in state space by X, then that element in state space is a realization. That is, at a point \omega \in \Omega, the value x = X(\omega) is called a realization of X