Homework 5 Section 4 1. Suppose the manager believes that u is smaller than $8 with probability 0.25, and that u is smaller than $12 with probability 0.75. Find a normal prior that matches this prior information. What are the mean and standard deviation values of the prior? The manager collects the fares for twenty fares and observes the values (in dollars): 7.5, 8.5, 9.5, 6.5, 7.0, 6.0, 7.0, 16.0, 8.0, 8.5, 9.5, 13.5, 4.5, 8.5, 7.5, 13.0, 6.5, 9.5, 21.0, 6.5. Assuming these fares are normally distributed with mean u and standard deviation o = 4, use your answer to the previous question to find the posterior distribution for the mean u. What are the mean and standard deviation values of the posterior? Round your answers to four decimal places. Mean =10 ,sd = 2.965204 i. Suppose that you are a visitor to New York City with little knowledge about the mean taxi cab fare. Select the least informative prior for u among the answer choices. 1i. Use the data from above and the prior from (i) to compute the posterior distribution for the mean fare. What are the mean and standard deviation values of the posterior? Round your answers to four decimal places