Task 1: Fit the model Yijlmi, o? ~ N( Hi, o? ), i = 1,...,n, j= 1, . ... J M=atBr;, i=1,...,n of = 9(ri | 70, 71), i=1,...,n a ~ some suitable prior B ~ some suitable prior 70 ~ some suitable prior 71 ~ some suitable prior to the data on pigs' weights used in the second exercise of the computer lab (so n = 9 and J = 48), where 9(2 70, 71) is either of the functions in (1), (2) or (3). In your submission, you should answer the following questions: 1. Which function g(x| 0, 71) did you use? Justify your choice in a sentence or two. 2. What priors did you put on the parameters o, 8, 7% and ~? 3. What are your Bayesian estimates for the parameters o, 8, 0 and ~? 4. Compare the posterior distributions of a and 8 with the posterior distributions of the corresponding parameters (i.e. intercept and slope of the regression curve) if you fit the model used in the computer lab to the data (i.e. an simple linear regression model with constant o?). Are there any noticeable differences? Comment briefly