Let X 1 ··· Xn be i.i.d.r.v.'s uniformly distributed on [0, l]. Let X (1) ··· X (n) be the ordered r.v.'s 0≦ X (1) ≦ X (2)···≦ X (n) ≦ l. We obtain the n + 1 intervals (X (i), X (i+1))n i=0, with X (0) = 0, X (n+1)= l of length Li = X (i+1) – X (i). Let N(c) be the number of intervals of length L i < c. We have where The study of Nc is of some interest in molecular biology and was studied in [3] where the author found a complicated expression for the probability for a randomly chosen segment to have a length less than or equal to c; he then obtains an approximation. From the experimental point of view, it seems more reasonable to work with the mean since one can obtain an unbiased estimator that way.