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Suppose we sample from a normal distribution with unknown mean μ but known standard deviation σ. The function f(x) = 1 on (-∞, ∞) can be used as an improper prior that is intended to represent no prior information about the mean (precision = 0).

a) Determine the general form of the posterior using this prior.

b) How do credibility intervals computed this way compare with confidence intervals computed using the known value of σ?

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