EC2303 Lecture 2
Definition








Experiment
o A process that leads to a single outcome that cannot be predicted with certainty
Sample point
o Most basic outcome of an experiment (small letter)
Sample space
o Collection of all its sample points
Integration
Ra
a
Rb
f (x)dx = 0
a
f (x)dx =
Rb
Rb
a [f (x) + g(x)]dx =
Rb
a
f (x)dx +
a
Rb
f (x)dx
Rb
a
Rb
g(x)dx
a
f (x)dx =
a
Rc
a
f (x)dx +
Rb
c
f (x)dx
b
f (x)dx = F (x) = F (b) F (a)
a
Descrptive Statistics & Probability
=
PN
CnN =
xi
Pn
N
x
=
N!
EC2303
Tutorial discussion #6.
Deadline for submission:
11:45am on next Monday (Oct 10) to my mail box (box number: 83, on 6th
oor of AS2, out of the main o ce of the Economics Department)
or
12 noon on next Monday into the submission box in lecture hal
EC2303 Foundations For Econometrics
Statistics for Business and
Economics: International
Edition, 7/e
A th
Author
:C
Carlson,
l
N
Newbold,
b ld
Thorne
Publisher : Pearson
ISBN
: 9780132471107
Available at NUS Coop @
Forum !
ttable
df
P
degrees of freedom for t curve
area under the t curve with df degrees
of freedom to the right of t(df)
Example:
P[t(2) > 2.92] = 0.05
P[2.92 < t(2) < 2.92] = 0.9
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
EC2303
Tutorial discussion #8.
Deadline for submission:
11:45am on next Monday to my mail box (box number: 83, on 6th oor of
AS2, out of the main o ce of the Economics Department)
or
12 noon on next Monday into the submission box in lecture hall.
1. Joh
EC2303
Tutorial discussion #1.
Reminder: Solutions to tutorial questions will not be posted onto IVLE. It is for your
own benet that you go to your tutorials prepared.
1. Recent studies suggest that smoking during pregnancy has an eect on the birth weight
EC2303
Tutorial discussion #9.
Deadline for submission:
Reminder: This is your last chance, no excuses to late submission will be
accepted
11:45am on next Monday to my mail box (box number: 83, on 6th oor of
AS2, out of the main o ce of the Economics De
= Assignment 2 =
EC2303 Foundations for Econometrics
AY2016/17, Semester 1
Please write your name, matriculation number, and tutorial group number on
the top of your submission. TWO (2) marks will be deducted if any of the above
information is missing. F
= Answers for Assignment 2 =
EC2303 Foundations for Econometrics
AY2016/17, Semester 1
1. n = 340, p = 61/340 = 0.179. The hypotheses are H0 : p 0.25 and Ha :< 0.25. = 0.05.
The test statistic is z = 3.006. Since 3.006 < 1.645 = z0.05 , we reject H0 .
is
Continuous Random Variables
= Lecture 4 =
Continuous Random Variables
Dr. LIU Zhengning
Department of Economics, NUS
AY2016/17, Semester 1
1 / 40
Continuous Random Variables
Liu (NUS): [email protected]
Agenda
1
The pdf and cdf for continuous RVs
2
The nor
Topics on the Mean and Variance
= Lecture 6 =
Topics on the Mean and Variance
Dr. LIU Zhengning
Department of Economics, NUS
AY2016/17, Semester 1
1 / 33
Topics on the Mean and Variance
Liu (NUS): [email protected]
Agenda
1
Understanding the mean and expec
Discrete Random Variables
= Lecture 3 =
Discrete Random Variables
Dr. LIU Zhengning
Department of Economics, NUS
AY2016/17, Semester 1
1 / 44
Discrete Random Variables
Liu (NUS): [email protected]
Agenda
1
Random variables (RVs)
2
Discrete RVs
3
Probabilit
EC2303 Lecture 6
Mean

Discrete RV

o
Continuous RV
o
Finding expected value for a function

Discrete RV
o
Finding E(aX + b) and E(aX + bY)

Constant can be pulled out
o
o
Variance

Discrete RV

o
Continuous RV

o
Formula
o
o
B is 0 as b is a const
Dealing with Two Random Variables
= Lecture 5 =
Dealing with Two Random Variables
Dr. LIU Zhengning
Department of Economics, NUS
AY2016/17, Semester 1
1 / 35
Dealing with Two Random Variables
Liu (NUS): [email protected]
Agenda
1
Joint probability distribu
Review for the Final Examination
Instructor: Juwon Seo
April 11, 2016
Several tips for the final exam.
There are five questions. Total mark is 50. The exam is a closed book
assessment.
The standard normal distribution table is attached. You may or may n
Review for the Final Examination
Instructor: Juwon Seo
April 11, 2016
Several tips for the final exam.
There are five questions. Total mark is 50. The exam is a closed book
assessment.
The standard normal distribution table is attached. You may or may n
Week 1: CDF & PMF
Probability Theory
Provides an analytic tool to understand
the underlying structure of data
Probability Mass Function (PMF)
" = ( = )
1. " 0 for all
2.
, " = 1
e.g. Suppose you roll a normal sixsided
die once and define to be the numbe
EC2303
Abbreviated solution to tutorial #4.
1.
Z
N (0; 1)
(a) P (Z >
1:32) = P (Z < 1:32) = 0:9066
(b) P (Z < 0:25) = 0:5987
(c) P ( 0:2 < Z < 1:22) = P (Z < 1:22) P (Z <
= P (Z < 1:22)
(d) P (Z <
[1
P (Z < 0:2)] = 0:3888
1:96) = P (Z > 1:96) = 1
0:2) = P
EC2303
Tutorial discussion #2.
Deadline for submission:
11:45am on Monday, Sept. 5 to my mail box (box number: 83, on 6th oor
of AS2, out of the main o ce of the Economics Department)
12 noon on Monday, Sept.5 into the submission box in lecture hall.
1.
EC2303
Tutorial discussion #7.
Deadline for submission:
11:45am on next Monday to my mail box (box number: 83, on 6th oor of
AS2, out of the main o ce of the Economics Department)
or
12 noon on next Monday into the submission box in lecture hall.
1. The
1.
Let
1
and
2
be true mean starting salaries for accounting and nance majors
respectively.
(a) X1
t11;0:05 psn1 1 = 7:72
(b) Step 1: H0 :
1
Step 2: since
1
2
and
= 0; Ha :
2
0:80
p
12
1:796
1
= 7:72
0:41; Interval: (7:31; 8:13)
6= 0
2
are unknown and n1
Lecture 4
Continuous probability distributions
1
Probability Distributions
Probability
y
Distributions
Discrete
Probability
Distributions
Continuous
Probability
Distributions
2
Continuous random variable
A continuous random variable is a variable that
ca
Lecture 1: Introduction
Statistics is concerned with
Collecting and presenting data to assist decision
making
Processing
g and analyzing
y g data
Obtaining reliable forecasts
1
Examples involving statistics
To inspect
T
i
t the
th incoming
i
i goods
d ffr
Lecture 5
Sampling Distributions
1
Population vs
vs. Sample
Population
a b
Sample
cd
b
ef gh i jk l m n
o p q rs t u v w
x y
z
c
gi
o
n
r
u
y
2
Inferential statistics
Population
Use parameters to
summarize features
Sample
Use statistics to
summarize featu
Lecture 6
Confidence
C
fid
IInterval
t
lE
Estimation
ti ti
for single population
1
Definitions
An estimator of a population parameter is
a rule
l or fformula
l th
thatt tells
t ll us h
how tto use th
the sample
l d
data
t to
t
calculate a single number
Lecture 2
Basic Probability
1
Introduction
We encounter uncertainties such as the following:
What is the likelihood that the Straits Times Index will be
i
increasing?
i ?
What is the likelihood that you will get 5 heads in 5 tosses of
coin?
What is the ch
Lecture 8
TwoSample hypothesis testing
and confidence intervals
1
An important estimation problem involves the
comparison of means of the two populations
populations.
For example, you may want to make
comparisons like these:
The average scores on Alevel
Lecture 7
Fundamentals of Hypothesis
T ti
Testing:
OneSample
O S
l T
Tests
t
1
Example 1
You are the manager of a manufacturing plant which produces
coffee The label on a large can states that the can contains three
coffee.
pounds. You want to make sure
EC 2303: Foundation for Econometrics
Fall 2012
Problem Set 5
Due on November 12 (Monday, 5:30 pm)
Rules for assignments:
(i) Show all the work leading to your answers.
(ii) You must write your name, matric number, and tutorial group number.
Missing any of
EC 2303: Foundations for Econometrics
Spring 2012
Final Examination
Problem 1 (5 points) The scores of the nal exam of 10 students in class
X is f88; 91; 88; 85; 82; 82; 94; 76; 71; 85g: Calculate the mean, median, mode,
variance, standard deviation, and
EC 2303: Foundation for Econometrics
Spring 2012
Final Examination
Answer Key
Problem 1 (5 points) The scores of the nal exam of 10 students in class X
is f88; 91; 88; 85; 82; 82; 94; 76; 71; 85g: Calculate the mean, median, mode, variance, standard devia
462 Chapter I 1 Comparisons Involving Proportions and a Test of Independence
Where do women most often buy casual clothing? Data from the US. Shopper Database
provided the following percentages for women shopping at each of the various outlets (The
Wall S
Formula Sheet
for EC 2303 Final Examination
Note for all random variables X, f (x) denotes the probability function (for discrete cases)
and the probability density function (for continuous cases).
Population mean:
=
PN
i=1
N
2
Population variance:
xi
=
;