Assume that X1, . . . ,Xn constitute an iid sample from a distribution with pdf f(x) ={ (pa)^p * (x)^(p1) if 0 < x <= a, and 0 otherwise

for some unknown parameters p > 0 and a > 0.

(a) Derive the maximum likelihood estimate for a. If calculus methods are used , perform a second derivative test.

(b) Derive the maximum likelihood estimate for p. If calculus methods are used, perform a second derivative test.

(c) Derive the equations that allow to find the method of moment estimators for p and a. Equations must explicitly contain p and a. Do NOT have to actually solve the equations.