A random process is a repeating process whose outcomes follow no describable deterministic pattern, but follow a probability distribution.
The term randomness is often used in statistics to signify well defined statistical properties, such as lack of bias or correlation. Random is different from arbitrary, because to say that a variable is random means that the variable follows a probability distribution. Arbitrary on the other hand implies that there is no such determinable probability distribution for the variable.
Randomness has an important place in science and philosophy.
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I came upon a duplicate hit -- "Steve Irwin." Other than the "Bestest Blog," this is the only time I come upon the same blog more than once as I continue my random sojourn through the "next blog" button.