A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functionsf(x),gi(x) (i= 1, 2, …,k) on a space (typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), whereXis a random variable taking values in , about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X>a), whereXis a real random variable with some of its moments given.
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J. F. C. Kingmán (1963) studied this question.
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