Use the following data: y = 71,28,5,2,2,1 Use a Beta(\alpha, \beta) prior for p then determine the Bayesian estimates (\hat{p}_k) that been obtain when selecting the hyper-parameters \alpha and \beta in the prior as \alpha = \beta = \gamma_k = 2^k, k = 1, 0, 1, 2, . . . , 18. Show the the Bayesian estimates then create a plot of the Bayesian estimates (\hat{p}_k) against log(\gamma_k). Use Rstan in R to answer the question, only. The STAN model must be run in STAN chunk in R markdown. Work created by attaching a separate stan file will receive penalty.