We will draw a sample of size n 11 from the normal distribution with mean and precision We will use a natural conjugate prior for the parameters (, ) from the normal gamma family with hyperparameters 0 2, 0 1, 0 3 5, and 0 2 The sample yields an average of Xn 7 2 and s2n 20 3 a Find the posterior h...

a The posterior hyperparameters are 1 2 35 11 722 11 663 1 2 11 ...

We will draw a sample of size n = 11 from the normal distribution with mean

Question:

We will draw a sample of size n = 11 from the normal with mean μ and precision τ. We will use a natural conjugate prior for the parameters (μ, τ) from the normal-gamma family with hyperparameters α0 = 2, β0 = 1, μ0 = 3.5, and λ0 = 2. The sample yields an average of Xn = 7.2 and s2n = 20.3.
a. Find the posterior hyperparameters.
b. Find an interval that contains 95% of the posterior of μ.
Distribution
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