We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Let X1 ··· 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))ni=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 Li < 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.
