# Definition:Experiment

## Definition

An experiment is defined as:

a course of action whose consequence is not predetermined.[1]

## Formal Definition

An experiment, which can conveniently be denoted $\mathcal E$, is a measure space $\left({\Omega, \Sigma, \Pr}\right)$ such that $\Pr \left({\Omega}\right) = 1$.

## Example

Let $\mathcal E$ be the experiment of throwing a standard $6$-sided die, to see whether the number thrown is greater than $4$.

• The sample space of $\mathcal E$ is $\Omega = \left\{{1, 2, 3, 4, 5, 6}\right\}$.
• The event space of $\mathcal E$ is: $\Sigma = \left\{{\forall \omega \in \Omega: \omega > 4}\right\}$.
$\displaystyle \forall \omega \in \Omega: \Pr \left({\omega}\right) = \frac 1 6$

## Also known as

An experiment is also known as a trial.