Random[ ] gives a uniformly distributed pseudorandom Real in the range 0 to 1.
Random[type, range] gives a pseudorandom number of the specified type, lying in the specified range. Possible types are: Integer, Real and Complex. The default range is 0 to 1. You can give the range min, max explicitly; a range specification of max is equivalent to 0, max.
Random[Integer] gives 0 or 1 with probability .
Random[Complex] gives a pseudorandom complex number in the rectangle with corners and .
Random[Complex, zmin, zmax] uses the rectangle defined by zmin and zmax.
Random[Real, range, n] generates an n-digit pseudorandom real number. Both leading and trailing digits may be chosen as 0.
Random gives a different sequence of pseudorandom numbers whenever you run Mathematica. You can start Random with a particular seed using SeedRandom.
See The Mathematica Book: Section 1.1.3 and Section 3.2.3.
Implementation Notes: see section A.9.4.
See also: $RandomState.
Related packages: Statistics`ContinuousDistributions`, Statistics`DiscreteDistributions`.