Homework 5 Section 3 Suppose two people, Pedro and Mia, have different prior beliefs about the average number of ER visits during the 10 pm - 11 pm time period. Pedro's prior information is matched to a gamma distribution with parameters a = 70 and p = 10, u = 7, sigma =0.8366 and Mia's beliefs are matched to a gamma distribution with a = 33.3 and B = 3.3 . p = 1.0091, sigma = 1.7486 Shown below is the number of ER visits during the period 10 pm to 11 pm for each day for a particular week at the hospital. Day Number of ER visits Sunday Monday Tuesday Wednesday Thursday Friday Saturday 1. Use the data shown above and the Pedro's prior to find the posterior distribution for the average number of ER visits. What are the alpha and beta values of Pedro's posterior? 11. Find the 95% credible interval for the average number of ER visits by using Pedro's posterior. Round your answer to one decimal place. III. Suppose one clueless hospital administrator states that the average number of ER visits during any evening hour does not exceed 6. Use Pedro's posterior to evaluate the validity of the administrator's statement. What is the probability that the administrator's claim is true according to Pedro's posterior