7.4.2 Prove that the family {m..y{} :a > 1, f} > 0} ofpriors given by Ir} \"\"1 {mac} (0) EHJIUJ) : (a '1}\"_l is a conjugate family of prion; with respect to sampling from the model given by the Uniform[0,ti] distributions with t? > 0. 7.4.3 Suppose that the statistical model is given by P0\") P00) 109(3) 100(4) - =a 1/3 [16 1,13 1/6 0 = b [/2 114 US 1/8 and that we consider the family of priors given by - Ida) rrrtb) r21 1/2 1/2 r22 1/3 2/3 and we observe the sample xi = 1.x; = 1.x; = 3' {a} If we use the maximum value of the prior predictive for the data to determine the value of r, and hence the prior, which prior is selected ltere'.' {b} Determine the posterior of 0 based on the selected prior