Homework 10

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.