6.3 Suppose that the target distribution is N(0.5, I ) truncated to the interval (0, m)

with density

(a) What is the normalizing constant of this target density?
@) Use the expression given in Equation (6.18) to obtain M = 5000 draws from the target density. Use this sample to find the posterior mean and variance.

(c) Set up a random-walk Metropolis-Hastings sampler to obtain M = SO00 values from the target density, adjusting the value of T as in problem 6.1 (b)
to ensun: that approximately 35-50 percent of the proposed values an‘
accepted. Did you need the normalizing constant of the target density to implement this algorithm?

(d) Find the posterior mean and standard deviation from the MCMC output and compare your results with those in part (b).