Random experiment

In probability theory , a random experiment (also known as a random process or random experiment ) describes an experiment that is carried out under precisely defined experimental conditions and has a random outcome. An experiment is understood here as a process in which several results can occur and in which an unpredictable, detectable result occurs, for example the tossing of a coin or a dice . The randomized experiment must be distinguished from this .

Although the result of each individual experiment is random, if a sufficiently frequent repetition is possible, regularities can be recognized that can be mathematically recorded. The variables of interest in a random experiment are called random variables .

properties

For an experiment to be a random experiment, it must have the following properties:

• There is a well-defined plan for implementation.
• All possible results of the experiment are known in advance.
• The outcome of each individual experiment cannot be predicted (randomness).

A random experiment can be unique and unrepeatable, or it can enable series of tests with equivalent tests that are independent of each other .

A random experiment can also have one or more stages . In the second case, the levels can be stochastically independent or dependent.

In computer programs, apparently random numbers, which are also referred to as pseudo- random numbers, are calculated with suitable algorithms to simulate random events .

One-step random experiment

Here the random experiment is carried out only once.

Examples :

• Throwing a die or a coin once.
• One-time drawing of a card from a shuffled deck.
• One-time rotation of a wheel of fortune or a top.
• Addressing an unknown person on the street with the question of the party that person voted for in the last election.

Multi-stage random experiment

Multi-step random experiments are random experiments that consist of several steps that are also random experiments in themselves. A simple example is repeating a single random experiment several times. Multi-level random experiments can often be illustrated by tree diagrams .

Examples:

• Roll the dice twice
• Drawing of several tickets from a lottery drum or several balls from an urn (with or without replacement)
• First you roll the dice and then as many balls are drawn from an urn as the number on the dice shows.

There are cases in which a multi-level random experiment can be replaced by a single-level experiment if the question is appropriate, in which the associated multi-level tree diagram can be replaced by a savings tree or even a single path.

• A die should be thrown until a "6" is scored, but no more than ten times.