Let Y. ... Y,, be a random sample from Y~EXP(1/8) with prior distribution for 8~EXP (1/B) where f is a known constant a) Find the joint density for Y, ... Y. 8. b) Use your result from part (a) to find the marginal density for Y, ... Y., c) Use your results from parts (a) and (b) to find the posterior density for 0 | Y, ... Y,, d) Use your result in part (c) to find the Bayes estimator for 0. (Hint: the Bayes estimator is