Realised Outcome

probability-theory

Definition

Realised Outcome

The realised outcome of a trial is the unique possible outcome that the trial actually produces. If the $i$-th trial has sample space $\Omega$, its realised outcome satisfies

$${\omega }_i\in \Omega .$$

Events

An event $A\subseteq \Omega$ occurs on trial $i$ precisely when the realised outcome belongs to it:

$$A\text{ occurs on trial }i⟺{\omega }_i\in A.$$

Two dice

Suppose two dice produce the physical result $(2,5)$. In a sample space that records both dice, the realised outcome is $\omega =(2,5)$. In a sample space that records only their sum, the same result is represented by $\omega =7$. The realised outcome therefore depends on the observation rule built into the model.