Probabilities of the deviation of the sample mean from its median

One investigates the asymptotic behavior of as n, where is the sample mean constructed from the independent, identically distributed random variables X₁...,X_n, >0. One considers the powerlike and the exponential rates of decrease of this probability.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 130–136, 1983.