# Definition:Experiment

## Contents

## 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 $\Pr \left({\Omega}\right) = 1$.

## Also see

## 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: $\Sigma = \left\{{\forall \omega \in \Omega: \omega > 4}\right\}$.

- The probability measure is defined as:

- $\displaystyle \forall \omega \in \Omega: \Pr \left({\omega}\right) = \frac 1 6$

## Also known as

An **experiment** is also known as a **trial**.

## References

- ↑ From 1986: Geoffrey Grimmett and Dominic Welsh:
*Probability: An Introduction*.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 4.2$: Trees and Probability - 1986: Geoffrey Grimmett and Dominic Welsh:
*Probability: An Introduction*... (next): $\S 1.1$: Experiments with chance