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random numbers

Random numbers are numbers that occur in a sequence such that two conditions are met: (1) the values are uniformly distributed over a defined interval or set, and (2) it is impossible to predict future values based on past or present ones. Random numbers are important in statistical analysis and probability theory.

The most common set from which random numbers are derived is the set of single-digit decimal numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. The task of generating random digits from this set is not trivial. A common scheme is the selection (by means of a mechanical escape hatch that lets one ball out at a time) of numbered ping-pong balls from a set of 10, one bearing each digit, as the balls are blown about in a container by forced-air jets. This method is popular in lotteries. After each number is selected, the ball with that number is returned to the set, the balls are allowed to blow around for a minute or two, and then another ball is allowed to escape.

Sometimes the digits in the decimal expansions of irrational numbers are used in an attempt to obtain random numbers. Most whole numbers have irrational square roots, so entering a string of six or eight digits into a calculator and then hitting the square root button can provide a sequence of digits that seems random. Other algorithms have been devised that supposedly generate random numbers. The problem with these methods is that they violate condition (2) in the definition of randomness. The existence of any number-generation algorithm produces future values based on past and/or current ones. Digits or numbers generated in this manner are called pseudorandom.

Statisticians, mathematicians, and scientists have long searched for the ideal source of random numbers. One of the best methods is the sampling of electromagnetic noise. This noise, generated by the chaotic movements of electrons, holes, or other charge carriers in materials and in space, is thought to be as close to "totally random" as any observable phenomenon.

This was last updated in September 2005

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how 1 and 4 averaged randomly provide  sqrt(11)?
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