# Random and Pseudorandom Numbers

## Random and Pseudorandom Numbers

numbers that can be regarded as the realization of some random variable. Usually realizations are considered of a random variable that is uniformly distributed on the interval (0, 1), or else approximations to such realizations are considered where the approximations have a finite number of digits in their representation. When such a narrow interpretation is used, a random number can be defined as a number made up of random digits. A random digit in a base-p number system is the result of an experiment with p equally likely outcomes; to each of the outcomes there corresponds one of the p digits. The experiments that generate the random digits are assumed to be independent.

The earliest sources of random digits were census tables and other tables of experimentally obtained numbers. The first tables of random digits were compiled in 1927 to meet the need of mathematical statistics for a random means of sample selection in the design of experiments. Subsequently, the development of the Monte Carlo method was accompanied by the invention of special experimental devices called random number generators. Most such generators make use of the noise of electronic devices.

The concept of pseudorandom numbers also originated in connection with the development of the Monte Carlo method. Such numbers can be generated through computation according to some given formula, or algorithm, but their properties are required to be similar to the properties of random numbers. In the most common algorithms, each succeeding number is computed from the preceding number. A sequence of pseudorandom numbers generated in this manner has a period; such sequences are thus essentially different from sequences of random numbers. Algorithms for generating pseudorandom numbers have not yet been fully investigated. Pseudorandom numbers are, however, preferred in the Monte Carlo method. The reason for this is that the properties of a sequence of pseudorandom numbers can be investigated by trial computation, and the experimental devices generate new sequences of random numbers each time they are used.

### REFERENCES

Ermakov, S. M. Metod Monte-Karlo i smezhnye voprosy. Moscow, 1971.
Sobol’, I. M. Chislennye melody Monte-Karlo. Moscow, 1973.

S. M. ERMAKOV

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