In this paper, we study the size of the membership-set for system identification in a probabilistic framework. Assuming that the regressors are persistently exciting and the measurement noise is a sequence of independent, identically distributed bounded random variables, lower and upper non-asymptotic probability bounds on the membership-set diameter are obtained. These bounds are used in the computation of the confidence intervals for interpolatory estimators. (C) 2003 Elsevier Ltd. All rights reserved.