Consider, once again, the model described in Example 7.5.10. Assume that n = 10 and the observed values of X1, . . . , X10 are
− 0.92, −0.33, −0.09, 0.27, 0.50, −0.60, 1.66, −1.86, 3.29, 2.30.
a. Fit the model to the observed data using the Gibbs sampling algorithm developed in Exercise 10. Use the following prior hyper parameters: α0 = 1, β0 = 1, μ0 = 0, and λ0 = 1.
b. For each i, estimate the posterior probability that Xi came from the normal distribution with unknown mean and variance.
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