Uniformly distributed random sequences

Random sequences are uniformly distributed if the random number generator which has created them is uniformly distributed, i.e. the probability that a particular value will be output is equal to the inverse value of all the possible values. Thus every value is equally probable.

Here we consider the case of a finite set of K random numbers Xi. Then the random sequence (Xi) is uniformly distributed, if the following conditions are valid for each random number Xi and for all numbers x:

P[Xi = x] = 1/K.

E.g.: The binary sequence (Xi) is uniformly distributed, if the following applies for all elements:

P[Xi = 0] = P[Xi = 1] = 1/2.

See: Uniform distribution.