This note considers the estimation of ordered means of two independent normal random variables. When estimating the smaller one of the two means, two simple (non-trivial) estimators are available: the minimum of the two normal random variables and the maximum likelihood estimator. For these two estimators we provide simple elementary derivations of bias and mean square error.

in this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. method is tested on problems to ensure the computational eciency. we have compared numerical results with results obtained by other method in literature. we conclude that propose method is computationally ecient and eective.

For a lower semicontinuous function f on a Banach space X, we study the existence of a positive scalar μ such that the distance function dS associated with the solution set S of f(x) ≤ 0 satisfies dS(x) ≤ μmax{f(x), 0} for each point x in a neighborhood of some point x0 in X with f(x) < for some 0 < ≤ +∞. We give several sufficient conditions for this in terms of an abstract subdifferential and...