The range order of a product of i transformations from a finite full transformation semigroup (Q1097972)

Let r be the rank of a product of i random transformations on a set of n elements. The author proves that the limit \(M_ i\) of the expected value of r/n as n goes to infinity is determined by \(M_{i+1}=1-e^{-M_ i}\), using results of Feller on the classical occupancy problem.