Let a sample (X1, X2, ..., Xn) be given from a uniform distribution on the segment [θ - 1, θ + 1]. Moreover, the prior distribution of θ is also uniform over the interval [a, b]. What is the Bayes estimator of θ for absolute error loss?
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Since the sample is from a uniform distribution on [θ-1, θ+1], the likelihood function is: L(θ|X1, X2, ..., Xn) = 1/(2n) if θ-1 ≤ Xi ≤ θ+1 for all i, and 0 otherwise. Show more…
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