A pseudorandom variable is a variable which is created by a deterministic procedure which takes random bits as input. The pseudorandom string will typically be longer than the original random string but less random. This can be useful for randomized algorithms.
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.  John von Neumann (1951)
(There are much better introductions out there. Please fix the above)
See also Random Variable, Extractor, Disperser, Expander.
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