Here is Wikipedias definition of random:
Randomness has somewhat disparate meanings as used in several different fields. It also has common meanings which may have loose connections with some of those more definite meanings. The Oxford English Dictionary defines "random" thus:
The fields of mathematics, probability, and statistics use formal definitions of randomness. In mathematics, a random variable is a way to assign a value to each possible outcome of an event. In probability and statistics, a random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution, such that the relative probability of the occurrence of each outcome can be approximated or calculated. For example, the rolling of a fair six-sided die in neutral conditions may be said to produce random results, because one cannot know, before a roll, what number will show up. However, the probability of rolling any one of the six rollable numbers can be calculated.
The term is often used in statistics to signify well-defined statistical properties, such as a lack of bias or correlation. Monte Carlo Methods, which rely on random input, are important techniques in science, as, for instance, in computational science.[1] Random selection is an official method to resolve tied elections in some jurisdictions[2] 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.
Randomness has somewhat disparate meanings as used in several different fields. It also has common meanings which may have loose connections with some of those more definite meanings. The Oxford English Dictionary defines "random" thus:
Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard.Closely connected, therefore, with the concepts of chance, probability, and information entropy, randomness implies a lack of predictability. Randomness is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.
The fields of mathematics, probability, and statistics use formal definitions of randomness. In mathematics, a random variable is a way to assign a value to each possible outcome of an event. In probability and statistics, a random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution, such that the relative probability of the occurrence of each outcome can be approximated or calculated. For example, the rolling of a fair six-sided die in neutral conditions may be said to produce random results, because one cannot know, before a roll, what number will show up. However, the probability of rolling any one of the six rollable numbers can be calculated.
The term is often used in statistics to signify well-defined statistical properties, such as a lack of bias or correlation. Monte Carlo Methods, which rely on random input, are important techniques in science, as, for instance, in computational science.[1] Random selection is an official method to resolve tied elections in some jurisdictions[2] 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.
