3. Consider the following Bayesian hierarchical model: in9 ~11\" N(9,1), i=1,...,10, are ~ No.72). 7-2 N Inn Gammall, 1). The following data were observed: y : {3.15, 0.97, 2.01, 0.38, 1.06, 1.60, 0.76, 1.03, 0.56, 2.83}. Use Gibbs sampling to sample from the posterior distribution of 9 (generate 100,000 samples and use 1,000 samples as burnin) and answer the following: 1. Plot the posterior density of 9. 2. Find the posterior mean of [9. 3. Find 95% equitailed credible interval of (9. Note: the density of a Int! Gamma.(a, b) is given by b\"/I'(a)$'a'le'b/$