# randomness

DEFINITION: In everyday parlance, “randomness” is the unpredictability of some individual event or the overall disorder, or patternlessness, of a sequence of events.

In mathematics, there are more precise definitions of “random” stemming from the fields of statistics and probability.

In statistics, a variable is random if it may assume any possible value (“outcome”) within a given probability (or “event”) space.

This definition, in turn, permits the calculation of a probability distribution for outcomes within the space.

ETYMOLOGY: The adjective “random” derives, via Middle English and Middle French, from the Old French verb randir, meaning “to run.”

The English and the French words are also akin to the Old High German verb rinnan, meaning “to run.”

USAGE: From the definitions presented above, it may be seen that even though individual random events are unpredictable, the frequency of different outcomes within the space (“trials”) may be predictable.

Perhaps the most common illustration of this combination of the randomness of individual events with the knowability of the probability of those events is the case of dice.

Each individual roll of the dice, of course, produces a purely random outcome.

However, the narrowly delimited space of possible outcomes determined by one or two, fair, six-sided, regular polygons (cubes) makes it a trivial matter to calculate the probability distribution of those outcomes.

The concept of randomness has numerous uses in the mathematical modeling of economic phenomena.

One of the most important of these is the notion of a “random walk.”