In Example 13.4, the conditional densities are f(x | y) = ye−xy and f(y | x) = xe−xy . Algorithmically, the Gibbs sampler in this situation would be Vi,Wi IID exponential(1), Xi = Vi/Yi−1, Yi = Wi/Xi....

In Example 13.4, the conditional densities are f(x | y) = ye−xy and f(y | x) = xe−xy . Algorithmically, the Gibbs sampler in this situation would be Vi,Wi IID exponential(1), Xi = Vi/Yi−1, Yi = Wi/Xi.

(a) Express Xn or Yn in terms of Vi,Wi (i = 1, ... , n) and Y0.

(b) Can anything be said about the convergence or divergence of Xn or Yn?