We are interested in the quantity $ = 01 - 00, where 0; e [0, 1], j = 0, 1, and so 6 6 [-1, 1]. Suppose we have a uniform prior on 8, i.e. 8 ~ Unif(-1, 1). 1. Is this prior on & sufficient to induce prior densities over both 0;? 2. Suppose 60 ~ Unif(0, 1) and 8 ~ Unif(-1, 1). What is p(0,), the density of 61 = 60 + 8? Indeed, with this setup, is it the case that p(1) = 0, Ve @ [0, 1]