1. Simple Metropolis: Normal Precision - Gamma. Suppose X = -2 was observed from the population distributed as / (0, - ) and one wishes to estimate the parameter 0. (Here 0 is the reciprocal of the variance o' and is called the precision parameter). Suppose the analyst believes that the prior on 0 is Ga(1/2, 1). Using Metropolis algorithm, approximate the posterior distribution and the Bayes' esti- mator of 0. As the proposal distribution, use gamma Ga(o, B) with parameters o, 8 selected to ensure efficacy of the sampling (this may require some experimenting)