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We require that the integrand be strongly convex with the same convexity parameter for each realization. Combined with a standard condition from the literature on stochastic programming, we establish non-asymptotic exponential tail bounds for the distance between the SAA solutions and the stochastic program\u2019s solution, without assuming compactness of the feasible set. Our assumptions are verified on a class of infinite-dimensional optimization problems governed by affine-linear partial differential equations with random inputs. 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