The discrete moment problem and linear programming

AbstractMoment problems, with finite, preassigned support, regarding the probability distribution, are formulated and used to obtain sharp lower and upper bounds for unknown probabilities and expectations of convex functions of discrete random variables. The bounds are optimum values of special linear programming problems. Simple derivations, based on Lagrange polynomials, are presented for the dual feasible basis structure theorems in case of the power and binomial moment problems. The sharp bounds are obtained by dual type algorithms and formulas. They are analoguous to the Chebyshev-Markov inequalities