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Stochastic simulations involve at least some random inputs. This introductory tutorial is meant to call attention to the need to model and generate such inputs in ways that may not be the standard or defaults in simulation-modeling software. There are both dangers involved with doing things inappropriately, as well as opportunities to do things better, making for more accurate and more precise results from simulations. Specific issues include possible dependence across and within random inputs, use of empirical distributions, and non-default use of the underlying random-number generator. Suggestions for novel ways of implementing some of these ideas in simulation-modeling software are offered.