MAT 3378 3X - Spring 2012
Assignment 1 - Solutions
[8]
Question 1:
1. (a) The response variable is the amount of wear of a tire. An explanatory
variable is the rubber compound. We can also imagine that the car
itself could have an eect on the wear of the

MAT3377
Fall 2015
Solution to Assignment 2
1. (i) In here n = 20 and Observations are
1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2.
Therefore an estimate for average number of cracked eggs/box is
y =
In this case
8+6
= 0.7.
20
n
X
1
s =
y

Mid-term test/ MAT3377
Surveys and Sampling
Fall 2015.
Time : 80 Minutes
Professor : M. Zarepour
Name :
Student Number :
Calculators are permitted. Write your answers in the space provided.
[15]1. Consider a stratified sampling with three strata and diffe

MAT3377
Fall 2015
Solution to Assignment 3
1. As it was discussed in the lectures we can write
(N 1)S 2 =
Nh
L X
X
(Yhi Y )2 =
h=1 i=1
Nh
L X
X
L
X
h=1 i=1
h=1
(Yhi Yh + Yh Y )2 =
(Nh 1)Sh2 +
L
X
Nh (Yh Y )2
h=1
Therefore
L
L
X
X
1f
S2
Nh (Yh Y )2
(1 f )

Mid-term trst/ MAT3377
Surveys and Sampling.
Time : 80 Minutes
Professor : M. Zarepour
Name :
Student Number :
Calculators are permitted. This is an open book exam.
1. A typed book consists of N=800 pages. A simple random sample of 12
pages are taken and

MAT3377
Fall 2015
Solution to Assignment 4
1. Part (i),
In
Define ri = yi /xi , i = 1, 2, . . . , n and Ri = Yi /Xi , i = 1, 2, . . . , N and R = Y /X.
Therefore
SRS we have, E(
r) = R.
N
Y
1 X Yi
.
E(
r R) =
N i=1 Xi X
On the other hand
N
1 X
= 1
Ri

MAT 3377, Fall 2015
Sampling and Surveys
Lectures: Monday 11:30-13:00 and Thursday 13:00-14:30 in DMS 1110.
Instructor: M. Zarepour, office: Room 207D, Mathematics and Statistics department, 585 King Edward Ave., Tel: 562-5800, Ext. 3503.
office hours : M

MAT3377
Dec. 20, 1999
Time: 3 Hours
Calculators are permitted. Test is open book.
Total Marks=100.
Make sure you have all 5 questions.
Name:
Student Number:
1
1. [20 marks] Which one of the the following statements are true ? Give your reason briefly.
(i)

MAT3377
Fall 2015
Solution to Assignment 5
Problem 1. First of all notice that
N
X
(i
i=1
N + 1 2 N (N 2 1)
) =
.
2
12
This can be proved by expanding the sum and using the fact that
N
X
=
i=1
N (N + 1)(2N + 1)
.
6
It is also easy to see that
N
1 X
N +1