Scores on IQ tests are designed to follow a normal distribution with a mean of IE") and a standard deviation of 15 when applied to the general population. Suppose we sample a people in a particular town and administer IQ tests for each person in our sample in order to estimate ,u, the town-specic IQ seore. Let Y; he the IQ score for the 11h person in the sample. For this question, you can assume that the standard deviation of IQ soores in this town is 15 {s2 = 225}, the number of observations is 2G {n = EU], and Elsa = 110'. Finally, suppose that the true value of ,u is 112. Of course this is usually the unknown parameter of interest, but for the sake of this question it will amume this value. Fbr this question you can use any result that we've discussed in class. You do not need to derive any result that we've oovered in class. a} First, let's use a normal model within the frequentist framework with a maximum likelihood estimator. So, the model is Y1, ...,Y2'] ~ NLu, :2 = 225} State the maximum likelihood estimate ML. {1 mark) b) Compute the value of BiosiML}, VmeL) and MSELE'LML} {3 marks] e} Determine the sampling distribution for ML. Show and justify your steps. (2 marks} d) Now, let's use a normal model within a Bayesian framework. We will assume the following model: Y1, rm\"; ~ Nip, 02 = 225] p. ~ N{lD,225] State posterior distribution of ,u. and oompute the Bayesian point estimate 111351.\". [=1 marks} e) Compute the value of Biesmgnym], Vortgam] and M Shimmy\"). Show and justify your steps. 1:? marks] f] Determine the sampling distribution for 33,\". Show and justify your steps. {3 marks] g) Compare the bias and MSE of our. and flanges. {2 marks}