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In: Science

Submitted By poomama

Words 831

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Words 831

Pages 4

Randomness means lack of pattern or predictability in events.[1] Randomness suggests a non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

Applied usage in science, mathematics and statistics recognizes a lack of predictability when referring to randomness, but admits regularities in the occurrences of events whose outcomes are not certain. For example, when throwing two dice and counting the total, we can say that a sum of 7 will randomly occur twice as often as 4. This view, where randomness simply refers to situations where the certainty of the outcome is at issue, applies to concepts of chance, probability, and information entropy. In these situations, randomness implies a measure of uncertainty, and notions of haphazardness are irrelevant.

The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory.

Randomness is often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input, are important techniques in science, as, for instance, in computational science.[2]

Random selection is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, if we have a bowl of 100 marbles with 10 red (and any red marble is indistinguishable from any other red marble) and 90 blue (and any blue marble is indistinguishable from any other blue marble), a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random. Random selection can be an official method to resolve tied elections in some jurisdictions[3] and is even an ancient method of divination, as in tarot, the I Ching, and bibliomancy. Its use in politics is very old, as office holders in Ancient Athens were chosen by lot, there being no voting.

Contents

[hide] * 1 History * 2 Randomness in science * 2.1 In the physical sciences * 2.2 In biology * 2.3 In mathematics * 2.4 In statistics * 2.5 In information science * 2.6 In finance * 2.7 Randomness versus unpredictability * 3 Randomness and religion * 4 Applications and use of randomness * 4.1 Generating randomness * 4.2 Randomness measures and tests * 5 Misconceptions and logical fallacies * 5.1 A number is "due" * 5.2 A number is "cursed" or "blessed" * 5.3 Odds are never dynamic * 6 See also * 7 Books * 8 References * 9 External links

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History

Main article: History of randomness

Ancient fresco of dice players inPompei.

In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.[4][5]

The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of the calculus had a positive impact on the formal study of randomness. In the 1888 edition of his book The Logic of Chance John Venn wrote a chapter on The conception of randomness that included his view of the randomness of the digits of the number Pi by using them to construct a random walk in two dimensions.[6]

The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. In the mid- to late-twentieth century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.

Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the deliberateintroduction of randomness into computations can be an effective tool for designing better algorithms. In some cases such randomized algorithms outperform the best deterministic methods.