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 and unknown precision given the parameter (, ) Use the normal gamma conjugate prior distribution with prior hyperparameters 0 0, 0 1, 0 1, and 0 60 The value of s2n is 2102 9 a Find the posterior distribution of (, ) b Compute Pr( 1 x)

Question: 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

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

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