Please use R

Let X1, ..., In ~ " (0, 0). Recall 0 = 2x is unbiased and consistent for 0 (but not sufficient). Part a) What are E(X) and V(X)? These are theoretical values that should contain 0. Part b) For large n, describe the sampling distribution of 2x. To do so, be sure to name the specific distribution and its corresponding parameters. Be careful: what are E(2x) and V(2x)? How do your answers from part a) help you answer this part? Part c) Use Monte Carlo simulation and your sampling distribution to verify that confidence intervals based on the central limit theorem and 0 = 2x meet the desired theoretical coverage. Be careful: in lecture 8B, we saw that some distributions like the Poisson are robust to small sample sizes, meaning even when n is relatively small, the CLT still works well. In this case, for Unif(0, 0) data, it's not very robust, so try making n relatively large. Keep in mind there is a difference between sample size n and Monte Carlo sample size NMC. Try n = 500 and NMC = 50, 000. Part d) Describe how changing k, n, and a affects the coverage. Try some larger and smaller values of k; larger and smaller values of n; and larger and smaller values of a