(Solution) - Suppose that a single observation X is to be taken -(2025 Original AI-Free Solution)

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Suppose that a single observation X is to be taken from the uniform distribution on the interval [? ? 1/2, ? + 1/2], the value of ? is unknown, and the prior distribution of ? is the uniform distribution on the interval [10, 20]. If the observed value of X is 12, what is the posterior distribution of ??