Random experiment

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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.

See also

Individual evidence

  1. ↑ Norbert Henze : Stochastics for beginners , 10th edition Springer Spectrum 2013, doi : 10.1007 / 978-3-658-03077-3 , p. 1.
  2. ↑ Büchter, Henn: Elementare Stochastik , p. 134, Springer Verlag Berlin 2006, ISBN 3-540-22250-2 .
  3. ↑ Wirths: The tree diagram , pp. 262–267, Pedagogical Zeitschriftenverlag Berlin, Mathematics in School 1999, Issue 5, ISSN  0465-3750 .

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