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Probability Models With Discrete And Continuous Parts, James E. Marengo, David L. Farnsworth
Probability Models With Discrete And Continuous Parts, James E. Marengo, David L. Farnsworth
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In mathematical statistics courses, students learn that the quadratic function E ((X – x )-squared) is minimized when x is the mean of the random variable X, and that the graphs of this function for any two distributions of X are simply translates of each other. We focus on the problem of minimizing the function defined by y ( x) = E ( IX – xI-squared ) in the context of mixtures of probability distributions of the discrete, absolutely continuous, and singular continuous types. This problem is important, for example, in Bayesian statistics, when one attempts to compute the decision …