Random Variable Realisation

Topics: Random Variable - Probability - Statistics

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(definition)

The realisation of a random variable is the value that is actually observed from it, the actual observation of what happened.

In other words, the realisation of a random variable is a specific value $x\in \mathbb{R}$ that is returned by our random variable (a function $X:\Omega \to \mathbb{R}$).

Random variables are denoted with uppercase letters (e.g. $X$), but their observations are denoted with lowercase letters (e.g. $x$).

Realisations are used when ordering random variables when we collect them as random samples.