Pls kindly hlp with my hw. I need it ASAP. Your help will be very much appreciated. Thanks

6. Let X follow a gamma distribution, with parameters a : 3 and A. A gamma distribution I'(a : 3, A) has density function: 3 A al /\\5t: 3 :r e for :r > 0 f($)== 0 otherwise Let 11:1, . . . ,mn be a random sample of size n from the above distribution. P. 4 of 5 MA2506 Probability 8: Statistics - Final exam (a) Find the Method of Moments estimator for A. [3 marks] (b) Find the Maximum Likelihood Estimator (ML..E) for A. Show ALL necessary steps. [6 marks] (0) Check that your answer in part (a) refers to a maximization. [2 marks] ((1) Suppose a researchers 15 measurements were as follows: 2, 5, 5, 7, 8, 8, 9, 12, 12, 12, 15, 16, 18, 18, 18 Estimate the parameter A. [2 marks]