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 (2 + 1' 4 4'4 ) and thus, the sampling model is a multinomial distribution: p(y|0) = - n! y1!yzlysly4! 2 where n = y1 + 92 + 93 + y4. Assume the prior distribution for # 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, 31 - yo) with probabilities (, "). Here yo can be viewed as another parameter (or a latent variable). Thus, n! yo y/1 - yo p(0, yoly) ox yo!(91 - yo)!yalyslyA! (2 ) " ( = " ) " ( 9 ) " 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: = 1 191-1