The University of Sydney
MATH1005 Statistics
maths.usyd.edu.au/MATH1005/
Summer/Winter/Semester2
Resource: R Commands
2016
The following R commands are used throughout MATH1005.
Once you have mastered these, it is easy to teach yourself other commands.
Us
The University of Sydney
MATH1005 Statistics
sydney.edu.au/science/maths/MATH1005
Semester 2
PRACTISE QUESTIONS FOR QUIZ 3
2015
Quiz3 consist of 5 questions requiring a numerical answer (answer to 2dp, if necessary).
The Quiz tests your basic skills in re
ECOS2002
Intermediate Macroeconomics
Lecturer: Matthew Smith
Topic 8
Open Economy Macroeconomics
School of Economics
Faculty of Arts and Social Science
Openness of an Economy
Openness can be considered to have three aspects:
1. Openness in trade. Depends
The University of Sydney
MATH1005 Statistics
Summer/Winter/Semester2 Topic4: Probability, Random Variables and Distributions
Probability
For 2 events A and B on the same sample space
A and B are mutually exclusive
P (A \ B) = 0
A and B are independent
P
The University of Sydney
MATH1005 Statistics
Summer/Winter/Semester2
Topic2: Numerical Summaries and Boxplot
2016
Numerical Summaries
Given a sample cfw_xi and ordered data cfw_x(i) for i = 1, . . . , n
n
1X
x
=
xi
n
i=1
!
n
n
n
X
2
X
X
1
1
1
s2 =
(xi x
The University of Sydney
MATH1005 Statistics
Summer/WinterSemester2
Topic3: Bivariate Data
2016
Bivariate Data
For paired observations cfw_(xi , yi ) for i = 1, . . . , n
summary statistics
y = a + bx
1 X X
xi
yi
n
i=1
i=1
n
1 X 2
xi = (n 1)s2x
n
i=1
n
1
The University of Sydney
MATH1005 Statistics
Summer/Winter/Semester2
Topic5: Discrete Random Variables
Discrete Random Variables
For a discrete random variable X
probability distribution
cfw_x, P (X = x) (often represented in table)
X
expected value or me
The University of Sydney
MATH1005 Statistics
Summer/Winter/Semester2 Topic4: Probability, Random Variables and Distributions
2016
Probability
For 2 events A and B on the same sample space
A and B are mutually exclusive
P (A B) = 0
A and B are independent
1
ECOS2002 Intermediate Macroeconomics
Tutorial Questions
Topic: National Accounting and the Keynesian Income-Expenditure Model
Tutorial 1 (Week 1: 1 August)
NB: The readings for this tutorial are indicated in Topic 1 of the reading guide.
1.
Assume a sim
The University of Sydney
MATH1005 Statistics
Summer/WinterSemester2
Topic3: Bivariate Data
2016
Bivariate Data
For paired observations cfw_(xi , yi ) for i = 1, . . . , n
summary statistics
y = a + bx
1 X X
xi
yi
n
i=1
i=1
n
1 X 2
xi = (n 1)s2x
n
i=1
n
1
ECOS2002
Intermediate Macroeconomics
Lecturer: Matthew Smith
Topic 1
National Accounting, the Keynesian
Income-Expenditure Model and Fiscal
Policy
School of Economics
Faculty of Arts and Social Science
The Circular Flow of Income and
Expenditure
The circ
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THE UNIVERSITY OF SYDNEY
MATH 1005 Statistics
sydnsy . adu . au/Bcisnce/maths/MATHiOOE
Semester 2 PRACTISE QUESTIONS FOR QUIZ 3 2015
Quiz3 consist of 5 questions requiring a numerical answer (answer to 2dp., if necessary).
The Quiz tests your basic skills
MATH1005 Tutorial Week 4 Solutions
n
1. Sxy = i=1 xi yi ( xi )( yi ) = 880.5 (25)(432) = 19.5.
n
12
From here we see the only possible correct answer is (c).
For the benet of later questions we compute the other two quantities as well:
2
n
x 2
Sxx = i=1 x
MATH1005 Tutorial Week 2 Solutions
1. To get the frequency distribution for the n = 31 values, simply count how often each distinct value
occurs:
No. of ice cream x
Frequency fx
Relative frequency fx /n
0
9
0.29
1
8
0.26
2
4
0.13
3
4
0.13
4
2
0.06
5
1
0.0
MATH1005 Tutorial Week 3 Solutions
1. (a) Denoting the values as x1 , x2 , . . . , xn (with n = 36), the mean is
n
1
1
x = n i=1 xi = 36 238.1 = 6.613889 6.61 (the indicates rounding). The variance can be
computed via the computing formula
s2
x
=
1
n1
n
1
THE UNIVERSITY OF SYDNEY
M ATH 1005 S TATISTICS
Semester 2
Assignment 1
2014
(1) Aim of Assignment
To explore the process of data analysis in Chapter 1: sourcing the data, creating numerical and graphical summaries, and interpreting the ndings.
(2) Marks
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Sample Quiz
MATH1005: Statistics
2014
Lecturers: Di Warren and Nicola Armstrong
Family name:
Other names:
SID:
Day:
Time:
Room:
Signature:
There are 15 multiple choice questions. Each question
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
Sample Quiz 1
MATH1005: Statistics
Family name:
Other names:
SID:
Day:
Time:
Room:
Signature:
There are 15 multiple choice questions. Each question is worth one mark.
Please ll in the correct a
The University of Sydney
MATH1005 Statistics
sydney.edu.au/science/maths/MATH1005
Semester 2
Tutorial Week 9
2011
Questions to try before the tutorial.
1. [Multiple Choice] Let X1 , . . . , Xn be a random sample of size n from a distribution with
1
mean a
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THE UNIVERSITY OF SYDNEY
Math1005 Statistics
Semester 2
Quiz 1a Week 8
2010
Name:
SID:
Time allowed: 40 minutes
For the multiple choice questions please circle the letter corresponding to your answer.
You will be provided with a blank sheet for rough work
8005A SEMESTER 2 2007
THE UNIVERSITY OF SYDNEY
FACULTIES OF ARTS, ECONOMICS, EDUCATION,
ENGINEERING AND SCIENCE
MATHlOOS
STATISTICS
November 2007 LECTURERS: R Kulik M Stewart
TIME ALLOWED: One and a half hours
This examination has two sections: Multiple C