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 +312 +313 +314. Assume the prior distribution for (9 to be U ml form(0, 1). To nd the posterior distribution of 6, a Gibbs sampling algorithm can be implemented by Splitting the rst category into two (yo, yl go) with probabilities G, 2). Here ya can be viewed as another parameter (or a latent variable). Thus, (9 , m _- (1)90 (erm (if (3)?\" (9)\" p 7310 y 110K311 yo)!y2!y3!y4! 2 4 4 4 4 ' 1. Derive the full conditional distributions of 6 and yo. 2. Implement Gibbs sampling in R, Matlab, Python, or Winbugs and obtain the posterior distribution of 0 (plot the density). 3. Find the estimate and 95% credible interval of 9. Hint