I'm struggling while trying to solve for this. All the infomation need are in the picutre.

Exercise 1 Let X1, X2, . . .Xn be a random sample of size n from a distribution with probability density function f($,9) = gee/9, a: > 0, 0 e 0 Note that, the moments of this distribution are given by This will be a useful fact for Exercises 2 and 3. (a) Obtain the maximum likelihood estimator of 6, 0. (This should be a function of the unobserved 3:; and the sample size n.) Calculate the estimate when 2:1 = 0.50, 2:2 = 1.50, 2:3 = 4.00, x4 = 3.00. (This should be a single number, for this dataset.) (b) Calculate the bias of the maximum likelihood estimator of t9, 0. (This will be a number.) {c} Find the mean squared error of the maximum likelihood estimator of l9, 0. (This will be an expression based on the parameter 6 and the sample size n. Be aware of your answer to the previous part, as well as the distribution given.) (cl) Provide an estimate for P[X > 4] when 3:1 2 0.50, x2 = 1.50, $3 = 400, 3:4 2 3.00