is asking for the R code to set up things for 4b. There is no output as such for (a). Here is an outline to set up the function. MCsim For a random sample of 50 observations from Poisson we have two ways to construct a 90% CI for the parameter 2. distribution, (1) Since the Poisson mean is , we can use the interval for the sample mean . (2) Since the Poisson variance is also , we can use the interval for the sample variance directly: . (a) Write a R-script to conduct a Monte Carlo study for the coverage probabilities of the two CIs. That is, to generate nsim=1000 such data sets from the Poisson distribution. Check the proportion of the CIs that contains the true parameter 2. (b) Run the Monte Carlo simulation for nsim-1000 runs, at three different parameter values: =0.1, =1 and =10. Report the coverage probabilities of these two CIs at each of the three parameter values. (c) Considering your result in part (b), which one of these two CI formulas should you use in practice? Can you explain the pattern observed in (b)?