Professor Wright postulates a statistical model for his students' aptitude test scores in which he thinks that his students' scores are normally distributed with unknown mean u and a variance of 90. Expert (or prior) opinion suggests that the average score is a normal random variable with a mean of 120 and a variance of 130. Thirty students of Professor Wright took the test and scored an average of 100. a. What is the posterior distribution for the average aptitude test score of Professor Wright's thirty students? b. What is the maximum likelihood estimate of H (PML)? c. What is the maximum a posteriori estimate of H (AMAP)? d. Construct a 90% confidence interval for u. e. Construct a 90% credible interval for u. f. Compare your answers in parts (d) and (e). Which interval is narrower