3. y Genetic study. A genetic study has divided n = 197 animals into four categories: (125, 18, 20, 34). A genetic model for the population cell probabilities is given by and thus, the sampling model is a multinomial distribution: n! p(y10) 2 where n = +Y2+yg+Y4. Assume the prior distribution for O to be Uniform(0, 1). To find the posterior distribution of O, a Gibbs sampling algorithm cau be implemented by splitting the first category into two (yo, yo) with probabilities Here yo can be viewed as another parameter (or a latent variable). Thus, n! p(O, yoly) 4 1. Derive the full conditional distributions of O and yo.