Realization (probability)

In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself is the process dictating how the observation comes about. Statistical quantities computed from realizations without deploying a statistical model are often called "empirical", as in empirical distribution function or empirical probability.

Conventionally, to avoid confusion, upper case letters denote random variables; the corresponding lower case letters denote their realizations.