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Consider the situation described in Exercise 7 of Sec. 8.5. Use a prior distribution from the normal-gamma family with values α0 = 1, β0 = 4, μ0 = 150, and λ0 = 0.5.
a. Find the posterior distribution of μ and τ = 1/σ 2.
b. Find an interval (a, b) such that the posterior probability is 0.90 that a < μ < b. |
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