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 01-0 1 -0 0 4 4 and thus, the sampling model is a multinomial distribution: n! y1 y2 D - A 1 A y3 A y4 p(y|0) = y1!yz!y3!y4! N 4 4where n = y1 + 92 + 93 + y4. 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 yo can be viewed as another parameter (or a latent variable). Thus, n! yo y1 -yo A y2 y4 p(0, yoly) x A y3 yo!(y1 - yo)!yz!y3!y4! N 4 4