(Solution) - Suppose that X1 Xn form a -(2025 Original AI-Free Solution)

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Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean ? and unknown precision ? , and also that the joint prior distribution of ? and ? is the normal-gamma distribution satisfying the following conditions: E(?) = 1, Var(? ) = 1/3, Pr(? > 3) = 0.5, and Pr(? > 0.12) = 0.9. Determine the prior hyperparameters ?0, ?0, ?0, and ?0.