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?