4. Let XX, be a random sample from Uniform(0, 0), a uniform distribution with an unknown endpoint 0. (a) Find the method of moments estimator (MME) for 0 and derive its mean, variance and mean square error (MSE). (b) Find the maximum likelihood estimator (MLE) for 0 and derive its mean, variance and MSE. (c) Compare the MME and MLE from above in terms of their mean square errors. (d) (R) Set the sample size as 25, do a simulation in R to compare these two esti- mators in terms of bias, variance and MSE. Include a side-by-side boxplot that compares their sampling distributions. (e) Consider the estimator a where is the MLE. Find a that minimises the MSE. Some information that might be useful: 6 E(X(1)) = n+1' E (X)) === 202 (n + 1)(n+2)' E (X(n)) = no n+1' E (X)) = n02 n+2