answer this question if possible

Suppose that X1, ...,Xn is a random sample from a distribution with the following pdf: f(:c|6) = $3Xp{7T(10g$ (9)2}, $ > o (a) Show that the maximum likelihood estimator of 6 is 9 = $22; log 333'. (7 pts) (b) Consider testing the hypotheses H0 : 6 = 0 vs. H1 : 6 7e 0. Show that the generalized likelihood ratio test is equivalent to rejecting H0 if |% 2;; log mil > c for some constant c. Hint: It will be a lot easier if you first make the substitution y; = 10g 937;, i = 1, ...,n. (8 pts) (c) If X N f(a:|6) as above, then Y = logX ~ N09, ). Explain. as precisely as possible, how you could use this fact to determine the value of c needed for a level a test. Note: Your explanation should involve the term 2(a/2). (5 pts)