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Please show work and answer, thank you Problem 5 (12 points): Let X be a discrete random variable whose possible values are 1, 2,3 with

Please show work and answer, thank you

Problem 5 (12 points): Let X be a discrete random variable whose possible values are 1, 2,3 with respective probabilities p1, p2, p3. If E[X ] = 2, find the values of p1, p2, p3 that maximize Var(X). (Hint: system of equations)

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