We will draw a sample of size n = 11 from the normal distribution with mean and precision . We will use a natural

We will draw a sample of size n = 11 from the normal distribution 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 distribution of μ.