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If we observe X = 1, what is the posterior distribution of the parameter theta? The posterior probability density is given by Bayes' rule: p(θ | X) = p(θ) * P(X | θ) / P(X) = 1 * θ / 0.5 = 2θ Note: The fact that P(X) = 0.5 could have been calculated using the method in part (b), or more simply by considerations of symmetry: since θ is uniformly distributed, X is equally likely to be 0 or 1.

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