STAT 409
Homework 1 (Answers)
n
Fall 2008
1.
Let X 1 , X 2 , , X n be a random sample of size probability density function
from the distribution with
f X (x ) = f X ( x ; ) = ( 1 ) 2
a)
ln x
x
,
x > 1,
> 1.
Find the maximum likelihood estimator of .
L()
STAT 409
Homework #2
(due Friday, September 12, by 4:00 p.m.)
Fall 2008
From the textbook:
4.7-4
Let Y n be the number of successes in n independent Bernoulli trials with probability p of success on each trial. By Chebyshevs Inequality, for > 0,
P
Yn
Yn
n
STAT 409
(due Friday, September 19, by 4:00 p.m.)
Homework #3
Fall 2008
1.
a)
Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function
3 f (x ) = 3 x 2 e x
x>0
> 0.
Find the sufficient statistic Y = u ( X 1 , X 2