f(x) = { 3. Let X1,..., Xn be a random sample from uniform distribution [0, 0] with density function 1 0, , 0 x 0; otherwise. = , We want to compare two estimators = 2X (method of moments estimator) and 02 = X (n) = max{X1, ..., Xn} (MLE). (a) Is unbiased? Why? Please provide some theoretical calculation. (b) Is unbiased? Why? Please provide some theoretical insight (if the calculation is too complicated for you). (c) Fix n = 20, 02. Generate 1,000 independent replicates of the sample and compare the biases of two estimators numerically. (d) Use the same data as in (c) to compare the variances and MSEs of two estimators numerically. What is your conclusion (which estimator is better in terms of MSE)? (e) Use the same data as in (c), plot densities of two estimators in a single figure. (f) Repeat (e) with different values of n, say, n = 2, 5, 20, 100. (g) Summarize your findings on the quality of these two estimators.