please show the work

Problem 4 Suppose X = (X1, . .., Xn) is a random sample from the density f(x; a, B) = QB ratI '[8,00 ) (x), a > 0, B>0. a) Find the Maximum Likelihood Estimator (MLE) for both a and B. Write the MLE for o in terms of T where T = log IIt=1 Xi Xn b) Consider testing Ho : a = 1, 3 >0 versus H1 : a # 1, B >0. Show that the likelihood ratio is given by the following n X(X) n-Tc) Show that the Likelihood Ratio test (LRT) has rejection region of the form {X : T(X)