1. Simple Metropolis: Normal Precision Gamma. Suppose X = 2 was observed from the population distributed as N (U, l) and one wishes to estimate the parameter {9. (Here {5' is the reciprocal of the variance 02 and is called the precision para-meter}. Suppose the analyst believes that the prior on 6 is Go f2, 1). Using Metropolis algorithm, approximate the posterior distribution and the Bayes" esti mator of {9. As the proposal distribution, use gamma Soa, ,3) with parameters oz, ,3 selected to ensure ellleaey of the sampling [this may require some experimenting). {a} Describe the posterior distribution of 6' using the Bayes7 estimator and the 97% HPD credible set. (b) Create two plots: one for the posterior density of {9 and one trace plot. For the trace plot, the Xaxis should be the iteration, and the Yaxis should be the observed walue of the chain at that iteration. {e} Report the acceptance rate of your proposal distribution. rThat is, what is the prob ability that the proposal was accepted when you ran the Metropolis algorithm?I