Dataset it provided below: 70.8 76.2 69.4 85.6 77.2 69.5 78.2 79.9 78.8 73 85.1 77.6 70.9 60.2 82.5 74.7 74.9 81.3 80.5 79 81.1 80.2 75.5 61.7 79.1 74.6 74 65.2 71.8 77.8 84.1 74.3 77.6 74.6 65.8 72.2 72.4 74.6 82.3 80.1 73.9 73.3 79.6 78.7 70.4 70.3 77.4 80.1 74.3 80.9 77.7 70.9 77.3 67.5 84.6 88.2 72.6 68 78.8 74.1 91 74.7 79.6 75.2 70 76.3 63 84.8 76 89.5 78.2 70.3 79.1 68.8 66.6 76.9 72 75 75.5 71.1 71.2 74.1 82.9 64.8 79 77.2 82.1 73 77.5 76.8 71.4 83.1 82.7 79.7 85.6 78.7 66.5 71.2 66.8 71.8

(b) (6 marks) Derive the posterior predictive distribution for a new score i, p(x x1, . .. , $100) Evaluate parameters in the posterior predictive distribution using the data from assignment3-prob1 . txt. Hint for (b)] A three-parameter version of a t distribution (Jackman, S. (2009)), denoted by t(v, a, b), has the pdf p(x(v, a, b) 1 (x - a)2 2 T(Z ) VTub V b