(b) The second prior formulation was 0; 1 a, B ~ Beta(a, B) a = $1/$2 B = (1 - $1)/$2 $1 ~ U(0, 1) 42 ~ U(0, 1000) (i) [2 pts] Independently simulate 1000 pairs (a, B) from their hyperprior, and produce a scatterplot of log(B) versus log(a). (ii) [2 pts] Using the simulated pairs (a, B), forward-simulate 0;, and produce a histogram of the result (an approximation of its marginal prior)