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An Optimal Upper Bound on the Tail Probability for Sums of Random Variables
2019
Theory of Probability and its Applications
Let s be any given real number. An explicit construction is provided of random variables (r.v.'s) X and Y for which sup P(X + Y s) is attained, where the sup is taken over all r.v.'s X and Y with given distributions. Let X and Y be random variables (r.v.'s) with given distributions. Let s be a real number. Then the tail probability P(X + Y s) for the sum X + Y of r.v.'s X and Y can be obviously bounded from above by the sum P(X x) + P(Y > s − x) of the "marginal" tail probabilities for X and Y
doi:10.1137/s0040585x97t989635
fatcat:chnhejb2fbasxkrp6glcac7mnm