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Un modele probabiliste utile en biologie moleculaire
Published online by Cambridge University Press: 14 July 2016
Abstract
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.
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- Copyright © Applied Probability Trust 1982
Footnotes
Ce travail a été subventionné par le programme FCAC du Ministère de l'Education du Québec et par une subvention du Conseil de recherches en sciences naturelles et en génie du Canada.