(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 known mean ? and unknown precision ? (? >0). Suppose also that the prior distribution of ? is the gamma distribution with parameters ?0 and ?0 (?0 > 0 and ?0 > 0). Show that the posterior distribution of ? given that Xi = xi (i = 1, . . . , n) is the gamma distribution with parameters ?0 + (n/2) and