Let X1 Xn be iid with pdf fx x1 0 x 1 0 a Find the met

Let X1, ..., Xn be iid with pdf f(x|) = x1 , 0 x 1, 0 < < .

(a) Find the method of moments (MM) estimator of .

(b) Find the maximum likelihood estimator (MLE) of .

(c) Suppose n = 1 and the hypothesis H0 : = 1 is to be rejected in favor of H1 : > 1 if x > 0.9. What is the test’s level of significance?

(d) What is the power function of the test (expressed as a function of hypothesized values of )?