Consider the random vector (X,Y,Z) with joint density proportional to

\[g(x,y,z)=4xz+6xy^2+8yz^3\]

when \(0<x,y,z<1\), 0 otherwise. Generate data from this rv

  1. using accept-reject
  2. using Metropolis-Hastings
  3. using the Gibbs sampler

Verify that your methods work by drawing the histogram of marginals and their densities.