[X] ~ ga (a) Show that full conditionals are normal and exponential, [oly, A] ~ N 72 T2 + 102" y+ do2 12 . 02 / n T 2 + 102 / n T2 + 102 [x/y, 0] ~ E T2 + (0 - 1 ) 2 272 (b) Jeremy models the score on his IQ tests as N(0, o?) with o? = 90. He places Cauchy Ca(110, v120) prior on 0. In 10 random IQ tests Jeremy scores y = [100, 106, 110, 97, 90, 112, 120, 95, 96, 109]. The average score is 103.5, which is the frequentist estimator of 0. Using Gibbs sampler described in (a) approximate the posterior mean and variance. Approximate 95% equi-tailed credible set by sample quantiles