A random sequence is a kind of stochastic process. In short, a random sequence is a sequence of random variables.

Random sequences are essential in statistics. The statistical analysis of any experiment usually begins with the words "let X₁,...,X_n be independent random variables...". The easiest way to talk about a situation when you can choose to make new measurements is to assume that an infinite sequence {X_i} is given, and that successive stages of the experiment you look at the first N terms of the sequence. Also, the statement of the central limit theorem (essentially that the average of a number of observations converges to the mean value) involves an infinite sequence of independent identically-distributed random variables.

Algorithmic information theory defines a random sequence as one that is shorter than any computer program that can produce that sequence (Chaitin-Kolmogorov randomness).

See also

• random number
• randomness
• pseudo-random number generator
• hardware random number generator
• Halton Sequences