2. Suppose that X1,..., X. are i. i.d. observations from the following probability density funetion: 1,4 (2) = - , *€14,00), (1,2) ERX (0,00).
(a) Find the joint) maximum likelihood estimators (MLES) An and on for p and v, respectively.
[2 marks
(b) Derive the asymptotic distribution of nlün - v) as n +00, where ûn is the MLE derived
in (a).
[3 marks
Hint: recall that if Y. %CE R has a constant limit, then Yo C.
(c) Suppose we are now interested in estimating g(v) = v's where r > 0 is known. Find an
MLE În of g() and derive the asymptotic distribution of vnlŷn – oſv)) as n + oo for
some function (v) which you should specify.
(1 mark]​