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Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability (or lack thereof) of events.

The Oxford English Dictionary defines 'random' as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard." This concept of 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 2 dice and counting the total, we can say 7 will randomly occur twice as often as 4. This view, where randomness simply refers to situations in which the certainty of the outcome is at issue, is the one taken when referring 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 the probability calculus. Source: wikipedia.org

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