4. Bayesian statistics: Suppose that the weight w of a female hippotamus is normally distributed with mean 1200 kg and standard deviation 200 kg. For the yearly medical assessment the zoo keeper was given the task of weighing the female hippotamus Nancy. The process produces random errors following a N(0, 1002) distribution. To compensate for the inaccuracy of the scale Nancy is measured three times yielding the following data points: = 1250 kg, x = 1300 kg, 3 = 1350 kg. (a) Describe the the prior distribution and the distribution underlying the likelihood. (4 marks) (b) What is the maximum likelihood estimate of Nancy's weight? (2 marks) (c) What is the implied sample size m corresponding to the prior? (2 marks) (d) Write down the Bayesian update formula for the mean parameter. (3 marks) (e) Compute the shrinkage intensity and the posterior expected value of Nancy's weight. (4 marks) 4. Bayesian statistics: Suppose that the weight w of a female hippotamus is normally distributed with mean 1200 kg and standard deviation 200 kg. For the yearly medical assessment the zoo keeper was given the task of weighing the female hippotamus Nancy. The process produces random errors following a N(0, 1002) distribution. To compensate for the inaccuracy of the scale Nancy is measured three times yielding the following data points: = 1250 kg, x = 1300 kg, 3 = 1350 kg. (a) Describe the the prior distribution and the distribution underlying the likelihood. (4 marks) (b) What is the maximum likelihood estimate of Nancy's weight? (2 marks) (c) What is the implied sample size m corresponding to the prior? (2 marks) (d) Write down the Bayesian update formula for the mean parameter. (3 marks) (e) Compute the shrinkage intensity and the posterior expected value of Nancy's weight. (4 marks)