Question: A random sample, X1,..., Xn, is drawn from a Pareto population with pdf (a) Find the MLEs of θ and v. (b) Show that the

A random sample, X1,..., Xn, is drawn from a Pareto population with pdf
A random sample, X1,..., Xn, is drawn from a Pareto

(a) Find the MLEs of θ and v.
(b) Show that the LRT of
H0: θ = 1, v unknown, versus H1: θ ‰  1, v unknown,
has critical region of the form {x: T(x) ‰¤ c1 or T(x) > C2}, where 0

A random sample, X1,..., Xn, is drawn from a Pareto

(c) Show that, under Ho, 2T has a chi squared distribution, and find the number of degrees of freedom.

Tn ,

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