2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130687This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are tighter and more broadly applicable than existing tail approximations.12 pages, 1 figureProbabilityStatistics Theory60E10; 62E17; 60F10; 60J50text