Outcome

probability-theory

Definition

Outcome

An outcome is one complete result represented by an element $\omega$ of the sample space of a random experiment. Before a trial, each $\omega \in \Omega$ is a possible outcome; after the trial, the result that actually occurred is the realised outcome:

$$\mathcal{E}\text{ specifies }\Omega ,\text{trial }i\text{ realises }{\omega }_i\in \Omega .$$

Possible Outcome

Definition

Possible Outcome

A possible outcome is a complete result admitted by the model of a random experiment, whether or not that result occurs in a particular trial. For a sample space $\Omega$,

$$\omega \text{ is possible}⟺\omega \in \Omega .$$

The sample space is therefore precisely the set of all possible outcomes.

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Realised Outcome

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

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

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