EC2303 Lecture 4
Continuous Random Variable


Probability distribution of CRV is a smooth curve or function fX(x). The probability that X falls
between two values, a and b, is the area under the cur
Lecture 5. Joint distribution I
Juwon Seo
Department of Economics
National University of Singapore
Feb 7, 2017
Juwon Seo (NUS)
Lecture 5. Joint distribution I
Feb 7, 2017
1 / 14
Announcement
I
I
I
Pro
= 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 =
= 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
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
Descrpt
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 noo
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
Availabl
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
1
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
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
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
EC2303 Lecture 3
Random Variables

(RV) assumes numerical values associated with the random outcomes of an experiment
Discrete Random Variables

Countable, can be finite or infinite
integer
Continuo
EC2303 Lecture 5
Joint Probability Distribution

When single RV are not sufficient to characterize
Probability distribution that defines the simultaneous behaviour of 2 or more random
variables
PDF
o
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 lett
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]
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): ecs
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]
Agen
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

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
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
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 s
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 6
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
Lecture 8a
Additional examples
1
Example 1
A professor is interested in whether
there is a difference in starting salaries
f college
for
ll
graduates
d t majoring
j i iin
accounting and finance. Mont
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
Lecture 4
Continuous probability distributions
1
Probability Distributions
Probability
y
Distributions
Discrete
Probability
Distributions
Continuous
Probability
Distributions
2
Continuous random varia
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 stat
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
summ
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 t
EC2303
Homework assignment #1.
Due date and time: 2pm on Tuesday, Feb 2nd. Late homework will get reduction
in marks.
Please put your nished homework into my mail box (box number: 83, on 6th oor
of AS