STAT 409
Fall 2012
Homework #2
( due Friday, September 14, by 4:00 p.m. )
1.
Let X 1 , X 2 , , X n be a random sample from the distribution with probability
density function
(
)
f X ( x ) = f X ( x ;
MATH/STAT 409
Homework # 3
due 09/20/2013
1. Let > 0 and let X1 , X2 , . . . , Xn be a random sample of size n from a distribution
with pdf
f (x; ) =
43
x , 0 < x < .
4
(a) Find the MLE .
(b) Is a con
STAT 409
Fall 2012
Name
Version A
ANSWERS
.
Exam 1
Page
Earned
Be sure to show all your work; your
partial credit might depend on it.
1
Put your final answers at the end of
your work, and mark them cl
MATH/STAT 409
Homework # 11
Due 12/06/2013
1.
7.2-8
2.
Metaltech Industries manufactures carbide drill tips used in drilling oil wells.
The life of a carbide drill tip is measured by how many feet can
STAT 409
Fall 2012
Name
Version B
ANSWERS
.
Exam 2
Page
Earned
Be sure to show all your work; your
partial credit might depend on it.
1
Put your final answers at the end of
your work, and mark them cl
MATH/STAT 409
Homework # 1
due 09/06/2013
1. Suppose = cfw_1, 2, 3 and the pdf f (x; ) is
= 1 : f (1; 1) = 0.6, f (2; 1) = 0.1, f (3; 1) = 0.1, f (4, 1) = 0.2
= 2 : f (1; 2) = 0.2, f (2; 2) = 0.3, f
MATH/STAT 409
Homework # 2
due 09/13/2013
1. 6.1-10
2. 6.1-18 (Hint: Use MoM)
3. Let X1 , X2 , . . . , Xn be a random sample from a distribution with pdf
fX (x; ) = ( + 1)(1 x) , 0 < x < 1, > 1.
Obtai
STAT 409
Fall 2012
Homework #4
( due Friday, September 28, by 4:00 p.m. )
1.
6.2-8 (
)
2.
6.2-12 (
)
3.
6.2-18 (
)
4.
6.4-4
The data in Exercise 6.2-12 that give results of a leakage test are repeated
STAT 409
Fall 2012
Homework #11
(due Friday, December 7, by 4:00 p.m.)
1.
Alex has a special coin he uses to make decisions in class. We do not know whether
the coin is fair or not, so we assign the f
STAT 409
Fall 2012
Homework #4
( due Friday, September 28, by 4:00 p.m. )
1.
6.2-8 (
a)
x = 46.42;
b)
s 2 = 41.682,
)
s 6.456,
t 0.05 ( 4 ) = 2.132,
46.42 2.132 6.456
5
46.42 6.156
or
( 40.264, 52.576
STAT 409
Fall 2012
Homework #1
( due Friday, September 7, by 4:00 p.m. )
1.
6.1-10 (
)
+
(d)
~1
p=
(a)
E( X ) = 1 p .
(b)
~
p equals the number of successes, n, divided by the number of Bernoulli
/
tr
STAT 409
Fall 2012
Homework #9
(due Friday, November 16, by 4:00 p.m.)
1.
Let X 1 , X 2 , , X 5 be a random sample of size
n=5
from a Poisson distribution
with mean > 0. We wish to test H 0 : = 2 vs.
STAT 409
Fall 2012
Homework #3
( due Friday, September 21, by 4:00 p.m. )
1.
Let > 0 and let X 1 , X 2 , , X n be a random sample from the distribution with
the probability density function
f X (x) =
STAT 409
Fall 2011
Homework #6
( due Friday, October 14, by 4:00 p.m. )
1.
In the past, only 30% of the people in a large city felt that its mass transit system is
adequate. After some changes to the
STAT 409
Fall 2012
Homework #5
( due Friday, October 12, by 4:00 p.m. )
1.
a)
6.3-2 (
)
Hint: equal variances
x
y
( y y)2
644
10983.04
623
6142.640625
493
2134.44
472
5274.390625
532
51.84
492
2769.39
MATH/STAT 409
Homework # 6
Due 10/18/2013
1.
6.4-4
The data in Exercise 6.2-12 that give results of a leakage test are repeated here:
3.1
3.3
4.5
2.8
3.5
3.5
3.7
4.2
3.9
3.3
Use these data t
MATH/STAT 409
Homework # 5
Due 10/18/2013
1.
6.4-4
The data in Exercise 6.2-12 that give results of a leakage test are repeated here:
3.1
3.3
4.5
2.8
3.5
3.5
3.7
4.2
3.9
3.3
Use these data t
STAT 409
Fall 2012
Name _
Extra Credit
(3 points)
No credit will be given without supporting work.
1.
Use mathematical induction to prove that
13 + 23 + 33 + n3 =
n 2 (n + 1) 2
4
for all positive inte
STAT 409
Fall 2011
Homework #5
( due Friday, October 7, by 4:00 p.m. )
1.
Consider Gamma ( , = usual ) distribution. That is,
f ( x; , ) =
1
( )
x 1 e x
,
0 < x < .
Suppose is known.
a)
Determine the
STAT 409
Fall 2012
Homework #10
(due Friday, November 30, by 4:00 p.m.)
1 2.
Let > 0 and let X 1 , X 2 , , X n be independent random variables, each with
the probability density function
f (x; ) =
n
R
STAT 409
Fall 2012
Homework #7
(due Friday, October 26, by 4:00 p.m.)
1.
A researcher wishes to determine whether the starting salaries of high-school math
teachers in private schools are higher than
STAT 409
Fall 2012
Name
ANSWERS
.
Version B
Quiz 5
(10 points)
Be sure to show all your work, your partial credit might depend on it.
No credit will be given without supporting work.
1.
A random sampl
STAT 409
Homework #8
Fall 2015
A. Stepanov
( due Friday, November 13, by 4:00 p.m. )
1 2.
Bert and Ernie noticed that the
following are satisfied when
Cookie Monster eats cookies:
(a)
the number of co
STAT 409
Fall 2012
Name
ANSWERS
.
Version A
Quiz 6
(10 points)
Be sure to show all your work, your partial credit might depend on it.
No credit will be given without supporting work.
1.
Consider a ran
STAT 409
Fall 2016
A. Stepanov
Name
ANSWERS
.
NetID _
Version A
Quiz 4
(8 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work
STAT 409
Fall 2015
A. Stepanov
Homework #1
( due Friday, September 4, by 4:00 p.m. )
Please include your name ( with your last name underlined ), your NetID,
and your discussion section number at the
STAT 409
Fall 2016
A. Stepanov
Name
ANSWERS
.
NetID _
Version A
Quiz 2
(8 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work
STAT 409
Fall 2016
A. Stepanov
Name
ANSWERS
.
NetID _
Version A
Quiz 1
(8 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work
STAT 409
Fall 2016
A. Stepanov
Name
ANSWERS
.
NetID _
Version A
Quiz 3
(8 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work
Data prep (excel)
Claims
Raw data set =>data prep (details added)=>analysis,
Where
pricing->set up premium
reserving->set aside $ for claims (ultimate loss)
numericals
excel pivot tables
Policy number