For a random sample of 50 observations from Poisson distribution, we have two ways to construct a 90% CI for the parameter . (1) Since the Poisson mean is 2, we can use the interval for the sample mean (X +10.05.49 1) 50 X X +to.95.49 1 50 (2) Since the Poisson variance is also 2, we can use the interval for the sample 49s 49s variance directly: (- 0.95,49 0.05, 49 (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 ). (b) Run the Monte Carlo simulation for nsim=1000 runs, at three different parameter values: 2=0.1, 2=1 and 2=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)