-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...

Extracted text: Let X1,..., X, a random sample with distribution f(x; 0) = (0 + 1)æº, 0 < 1,="" with="" parameter="" 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