# Random number

The result of special random experiments is called a random number .

Random numbers are required in various statistical methods , e.g. B. when selecting a sample from a population , with the random distribution of test animals to different test groups ( randomization ), with the Monte Carlo simulation and the like. a.

There are various methods for generating random numbers. These are called random number generators . A decisive criterion for random numbers is whether the result of the generation can be viewed as independent of previous results or not.

## Real random numbers and pseudo-random numbers

Real random numbers are generated with the help of physical phenomena: coin tossing, dice, roulette , noise from electronic components, radioactive decay processes or quantum physical effects. These methods are called physical random number generators , but are very time-consuming or technically complex.

In real applications, a sequence of pseudo- random numbers is often sufficient, i.e. seemingly random numbers that are generated using a fixed, reproducible process. So they are not random because they can be predicted, but they have similar statistical properties (even frequency distribution , low correlation ) as real random number sequences. Such procedures are called pseudo random number generators .

For other purposes, e.g. B. when generating cryptographic keys, however, real random numbers are required.

## Standard random numbers

Standard random numbers should be able to be regarded as the realization of independent , uniformly distributed random variables . ${\ displaystyle u_ {1}, \ dotsc, u_ {n}}$ ${\ displaystyle [0; 1]}$ One method for generating such sequences is called a standard random number generator. Such generators should be fast and the sequences generated should be easily reproducible in a straightforward manner. Most standard random number generators are congruence generators .

The simulation lemma enables, at least in principle, the generation of random numbers from other univariate distributions from standard random numbers with the aid of the inversion method .