Based on original algorithms developed at Wolfram Research, the Wolfram Language's core randomness generation is both highly efficient and of exceptional quality. The Wolfram Language can produce both discrete and continuous randomness, with a wide range of distributions conveniently specified in symbolic form.

RandomInteger — random integer or array of integers

RandomReal — random real or array of reals

RandomComplex — random complex numbers

RandomVariate — nonuniform random variate or array of variates

RandomPoint — random point in a region

RandomChoice — random choices from a list

RandomSample — random samples or permutation of a list

RandomPrime — random prime number

RandomColor  ▪  RandomImage  ▪  RandomGraph  ▪  RandomPermutation  ▪  RandomEntity  ▪  RandomWord

Statistical Distributions »

NormalDistribution  ▪  StudentTDistribution  ▪  PoissonDistribution  ▪  ...

SeedRandom — seed and pick method

RandomSeeding — option for random seeding within a particular function

BlockRandom — make random number generation localized

RandomGeneratorState — symbolic representation of a random number generator

$RandomGeneratorState — the state of the current random number generator

ShiftRegisterSequence — generate pseudonoise sequences