Question: Consider a random sample from the distribution x] = 9.172, 1' 2 6'. We wish to test H0 : I9 1: :90 V3 H] I

Consider a random sample from the distribution x] = 9.172, 1' 2 6'. We wish to test H0 : I9 1: :90 V3 H] I l9 3' 90. (a) Find the overall MLE, 9. (1:) Find the restricted MLE, an. (e) Can you use these estimators, d\" and d, to build an asymptotic LRT? Why or why not? If so, what is the test? (d) Find LRT statistic and invert the rejection region so that it will have the one of the following forllls: {T c}. or {T c: (:1 or T > {:2} (c) Find the appropriate minds) of r: such that this test has size (x. (f) Compare this test to the UMP test found previously

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