This is a Gibbs sampler question with a little bit of coding that I would love an explanation and answer to thanks.

Problem 4 Program the Gibbs sampler to sample the threedimensional vector (X 1 , X 2, X 3) with probability mass function equal to: P(X1 = $13X2 = $23X3 = 333) = 2m2m2+3m3 1 231:1 232:1 233:12'9fy2-I-3y3 if 1 S 1 E 2: 1 S 2 E 2! 1 S :33 S 2 0 else a) Using for rst point x0 = (1,2,1),calculate manually the rst sample 3:1 = (ml, 3:21,, 33%) by using the uniform variate vector u1 = (mining) = (0.25,0.3,0.7) b) Program the algorithm, and output b.1) the source code or pseudo-code b2) the numerical value of the Monte Carlo estimator of E[X1X2X3] using N =1000 scenarios. Note: this is NOT a traditional use of the Gibbs sampler, but introducing realistic applications of the Gibbs sampler is outside the scope of the course. This is used a lot in Bayesian networks. This problem will not be tested in the midterm