Show how the results in

(a) in the previous exercise generalize to estimating Poisson parameters for c groups in the one-way layout. For fixed gamma hyperparameters, show that the estimate of ????i for group i is a weighted average of ȳi and the mean of the gamma prior distribution. When those hyperparameters are estimated using the marginal negative binomial distribution, show that empirical Bayes estimates shrink {ȳi} toward the overall ȳ.