Definition:Experiment

Context
Probability Theory.

Definition
An experiment (or trial) is defined as:
 * a course of action whose consequence is not predetermined.

An experiment $$\mathcal E$$ can be formulated mathematically by means of a probability space, which consists of:


 * The sample space: that is, the set of all possible outcomes of the experiment;


 * The event space: that is, the list of all the events which may occur as the consequences of the experiment;


 * The probability measure on the event space: that is, the likelihood of the happening of each of the events in the event space.

With this definition, $$\mathcal E$$ 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: $$\Sigma = \left\{{\forall \omega \in \Omega: \omega \le 4, \omega > 4}\right\}$$.


 * The probability measure is defined as: $$\forall \omega \in \Omega: \Pr \left({\omega}\right) = \frac 1 6$$.