Exercise 1 Input modeling and input uncertainty, simulation programming and experi- ments: For a Poisson distribution with paramcter Xe, dcrive an approximate 100(1-a) percent confident interval for given the data X1, X2, X, (a) Find the MLE X. Use the asymptotic normality to construct the confidence intcrval (b) Use the parametric bootstrap to construct the confidence interval. c) Develop the Python simulation code to estimate the coverage and expected width of confident intervals from parts (a) and (b) for n -5, 10, 100, 1000. (Hint: Gencrate 1000 rcplications. In cach replication, gencrate n rcal-world data from the underlying true Poisson distribution, say with parameter 1. Construct the confident intervals by using both approaches. Then, estimate the coverage and expected width by using these 1000 confident intervals from all replications) Exercise 1 Input modeling and input uncertainty, simulation programming and experi- ments: For a Poisson distribution with paramcter Xe, dcrive an approximate 100(1-a) percent confident interval for given the data X1, X2, X, (a) Find the MLE X. Use the asymptotic normality to construct the confidence intcrval (b) Use the parametric bootstrap to construct the confidence interval. c) Develop the Python simulation code to estimate the coverage and expected width of confident intervals from parts (a) and (b) for n -5, 10, 100, 1000. (Hint: Gencrate 1000 rcplications. In cach replication, gencrate n rcal-world data from the underlying true Poisson distribution, say with parameter 1. Construct the confident intervals by using both approaches. Then, estimate the coverage and expected width by using these 1000 confident intervals from all replications)