Solve the following problem:
Calculate the mean of a gamma G(4.3, 6.2) random variable using
a. Accept-Reject with a gamma G(4, 7) candidate;
b. Metropolis-Hastings with a gamma G(4, 7) candidate;
c. Metropolis-Hastings with a gamma G(5, 6) candidate. In each case, monitor the convergence across iterations.