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Consider the calorie count data described in Example 7.3.10 on page 400. Now assume that each observation has the normal distribution with unknown mean μ and unknown precision τ given the parameter (μ, τ). Use the normal-gamma conjugate prior distribution with prior hyperparameters μ0 = 0, λ0 = 1, α0 = 1, and β0 = 60. The value of s2n is 2102.9.
a. Find the posterior distribution of (μ, τ).
b. Compute Pr(μ > 1|x). |
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