Homework 11 for BST 631: Statistical Theory I – Problems, 11/16/2006
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Due Time: 5:00PM Thursday, on 11/28/2006.
Problem 1 (10 points). Book problem 5.2.
Problem 2 (10 points). Book problem 5.12.
Problem 3 (10 points). Book problem 5.15.
Problem 4 (10 points). Book problem 5.16.
Problem 5 (20 points). Book problem 5.17.
Problem 6 (10 points). Book problem 5.21.
Problem 7 (10 points). Book problem 5.22.
Problem 8 (20 points). (2004 January Qualify Exam Problem 1)
Consider the pdf
1
(1)
1
() ,1 , 0.
c
fx x x c
c
−+
=≤<∞>
(1) Show that the distribution of
X
is a member of the exponential family.
(2) Let ln( )YX=.Find the distribution of Y.
(3) Find the first and second moments of Y.
(4) Derive the moment generating function of Y.