Suppose we observe data (yams) E R2, 1' = 1,...,n as in the dataset dt_HW6.csv that we view as independent realizations from a simple linear regression model Y; ~ N030 + lming), i = 1, . . .,n, where a is assumed known and set to 0' = 1. Our interest is in the parameter ,Bol, and as prior distributions, we assume that 60 ~ NH}, 101), [31 ~ N(0,Tl'1), with To = 7' 1 = 103. 1. Derive the expression of the posterior density of g, 61. 2. Use the Metropolis algorithm to sample from the posterior distribution and compute a 95% posterior interval for ,80 and 61. How condent are you that these condent intervals are accurate? Explain