3. Let X1, X2,. Xn be a random sample of size n from a Poisson distribution with parameter Li31 (a) Use moment generation function technique to determine the distribution of T (b) Find the maximum likelihood estimator for f(0) =e-d in terms of T

Let X1,..., X, a random sample with distribution f(x; 0) = (0 + 1)æº, 0 -1. (a) Find the method of moments estimator of 0. (b) Show that the method of moments estimator is consistent. (c) Find the maximum likelihood estimator of 0. (d) takes value 0 = 1.2. Use the parametric bootstrap method to obtain a 95% revised bootstrap percentile confidence interval using the maximum likelihood estimate. Make sure to include a plot of the bootstrapped values and an interpretation of your confidence interval. Given a sample of size n = 500, suppose that the maximum likelihood estimate of 0