Consider the same scenario as in the previous problem. Based on the same data model for the y = 40 unsuccessful calls observed yesterday, a Bayesian analyst determines the following posterior for : (a) (b) (c) (d) |y=40 Beta(=6,=50) [1 pt] What specific prior did the analyst use? (Specify either an expression proportional to its density, or a distribution's name and constants.) [2 pts] Based on this posterior, approximate the posterior mean and posterior standard deviation of . (Retain at least three significant digits.) [2 pts] Based on this posterior, approximate a 95% equal-tailed (Bayesian posterior) credible interval for . (Retain at least three significant digits.) [1 pt] Based on this posterior, approximate the posterior probability that 0.1. (Retain at least three significant digits.) 1 3. (e) [1 pt] Based on this posterior, approximate the posterior predictive probability that, compared to yesterday, the salesperson will need to make strictly fewer calls today to fulfill today's quota of 5 successful calls. (You may assume that the numbers of unsuccessful calls today and yesterday are conditionally independent. Retain at least three significant digits in your numerical answer.)