Remark 

(1) The distribution given by is called a uniform distribution over the interval [0,1].

(2) The above result is particularly important in simulating a random variable with a particular distribution function.
      We assumed to be one-to-one function for invariability. However, the result is more general  -
                 the random variable defined by the distribution function of any random variable is uniformly distributed
                 over [0,1]
      For example, if is a discrete RV,