1. The lm 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 1' are independent with a common probability p;- of being positive (depending on the movie). Assume a U(0, 1) prior on each 19. (a) [4 pts] Determine the posterior distribution of p1 and of 302 (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 sufciently accurate.)