This preview shows pages 1–2. Sign up to view the full content.
December 18, 2009
MATH 230 Homework #3
(Due: December 29, Tuesday)
{Please, submit your homework to my office (SA105) by 17:30 p.m.}
1.
Show that the sample variance, S
2
is an unbiased estimator for population
variance σ
2
.
2.
If
Y
has a binomial distribution with parameters n and p
a)
Show that
Y/n
is an unbiased estimator of
p.
b)
To estimate the variance of
Y
, we generally use
n(Y/n)(1Y/n)
. Show that this
estimator is a biased estimator of
Var(Y).
c)
Modify
n(Y/n)(1Y/n)
to form an unbiased estimator of
Var(Y).
3.
The interarrival times (in minutes) at a certain checkout counter during a
weekday is uniformly distributed over the interval ( 0,
θ
), where
θ
is unknown
interarrival time. Suppose
n
X
X
X
,
,
,
2
1
denote a random sample of
interarrival times,
a)
Find an unbiased estimator,
θ
ˆ
of
that makes use of the entire sample.
b)
Find variance of
ˆ
.
4.
The lifetimes of a component are assumed to be exponential with parameter β.
10 of these components were placed on test independently. The only data
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/22/2011 for the course CS 101 taught by Professor Dat during the Spring '11 term at Bilkent University.
 Spring '11
 dat

Click to edit the document details