Could you show the programming as well? Thank you!

9. Let X1, ...,X.,1 ~ Normal(u,1). Let 0 = e\" and let '9'\": sf be the MLE. Create a data set (using a = 5) consisting of n=100 observations. 9. Parametric Inference (a) Use the delta method to get 5% and a 95 percent condence interval for 6. Use the parametric bootstrap to get 5% and 95 percent condence interval for 6'. Use the nonparametric bootstrap to get 5% and 95 percent condence interval for I9. Compare your answers. (b) Plot a histogram of the bootstrap replications for the parametric and nonparametric bootstraps. These are estimates of the distribution of (3', The delta method also gives an approximation to this distribution namely, Normal(,se2). Compare these to the true sampling distribu- tion of 3 (which you can get by simulation). Which approximation parametric bootstrap, bootstrap, or delta method is closer to the true distribution