STAT 578 - Advanced Bayesian Modeling - Fall 2019 Assignment 1 1. The film review aggregator website rottentomatoes. com publishes ranked lists of movies based on the number of positive critical reviews out of a total number counted for each movie. See, for example, https://www. rottentomatoes. com/top/bestofrt/?year=2018. Because the site uses an "Adjusted Score," a movie with a higher approval percentage sometimes ranks lower on the list. Consider the following hypothetical scenario: Movie 1: 150 positive reviews out of 200 (75%) Movie 2: 4 positive reviews out of 5 (80%) Assume that reviews of Movie i are independent with a common probability p; of being positive (depending on the movie). Assume a U(0, 1) prior on each pi. (a) [4 pts] Determine the posterior distribution of p1 and of p2 (separately). (b) [3 pts] Which movie ranks higher according to posterior mean? According to posterior median? According to posterior mode? Show your computations. (For median, use R function qbeta. For mean and mode, use formulas in BDA3, Table A.1. Do not use simulation, as it may not be sufficiently accurate.)