Consider the target density
![1062_60d6a187-051e-4cc3-baa5-c670df41c27e.png](https://secure.tutorsglobe.com/CMSImages/1062_60d6a187-051e-4cc3-baa5-c670df41c27e.png)
a. Show that f integrates to 1 and that it is a bimodal density.
b. Implement a normal random walk Metropolis-Hastings algorithm with a small variance like .04, and use plot.mcmc, cumuplot, and heidel.diag to assess the convergence when starting from x = - 2 and x = 2.
c. Compare those assessments with an on-line evaluation of the integral R f(x) d x based on the MCMC sample thus produced.