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Computing Best-Possible Bounds For The Distribution Of A Sum Of Several Variables Is Np-Hard, Vladik Kreinovich, Scott Ferson
Computing Best-Possible Bounds For The Distribution Of A Sum Of Several Variables Is Np-Hard, Vladik Kreinovich, Scott Ferson
Departmental Technical Reports (CS)
In many real-life situations, we know the probability distribution of two random variables x1 and x2, but we have no information about the correlation between x1 and x2; what are the possible probability distributions for the sum x1+x2? This question was originally raised by A. N. Kolmogorov. Algorithms exist that provide best-possible bounds for the distribution of x1+x2; these algorithms have been implemented as a part of the efficient software for handling probabilistic uncertainty. A natural question is: what if we have several (n>2) variables with known distribution, we have no information about their correlation, and we are interested …