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 1 0 1-0 1-0 0) 2 4' 4 '4 '4) and thus, the sampling model is a multinomial distribution: n! p(y|0) = - y1!yz!y3!y4! 2 where 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 (?, 4). Here yo can be viewed as another parameter (or a latent variable). Thus, n! p(0, yoly) x yo!(y1 - yo)!yz!y3!y4! 1. Derive the full conditional distributions of 0 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 0. Hint: NOIF