3. Genetic study. A genetic study has divided n = 197 animals into four categories: y = (125, 18, 20, 34). A genetic model for the population cell probabilities is given by 0 1-0 1-0 0 + and thus, the sampling model is a multinomial distribution: n! 1/2 p(y|0) = 31!yz!ya!ya! 2where n = y1+ 92 + y3+ y. Assume the prior distribution for 0 to be Uniform (0, 1). To find the posterior distribution of 0, a Gibbs sampling algorithm can be implemented by splitting the first category into two (yo, y1 - yo) with probabilities (, "). Here y, can be viewed as another parameter (or a latent variable). Thus, n! 1/2 1/4 p(e, yoly) ox yo!(31 - yo)!yz!ya!ya! 1. Derive the full conditional distributions of e and yo