Statistical randomness

A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal die roll, or the digits of π (as far as we can tell) exhibit statistical randomness.Statistical randomness does not necessarily imply "true" randomness, i.e., objective unpredictability. Pseudorandomness is sufficient for many uses.A distinction is sometimes made between global randomness and local randomness. Most philosophical conceptions of randomness are "global" — they are based on the idea that "in the long run" a sequence would look truly random, even if certain sequences would not look random (in a "truly" random sequence of sufficient length, for example, it is probable that there would be long sequences of nothing but zeros, though on the whole the sequence might be "random"). "Local" randomness refers to the idea that there can be minimum sequence lengths in which "random" distributions are approximated. Long stretches of the same digits, even those generated by "truly" random processes, would diminish the "local randomness" of a sample (it might only be locally random for sequences of 10,000 digits; taking sequences of less than 1,000 might not appear "random" at all, for example).
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