For the normal-Cauchy Bayes estimator
solve the following questions when x = 0, 2, 4.
a. Plot the integrands, and use Monte Carlo integration based on a Cauchy simulation to calculate the integrals.
b. Monitor the convergence with the standard error of the estimate. Obtain three digits of accuracy with probability .95.
c. Repeat the experiment with a Monte Carlo integration based on a normal simulation and compare both approaches.