7.1
Seven
I NTRODUCTION
There are many natural random variables whose set of possible values is uncountable. For example, consider a random variable which denotes the lifetime of an electrical appliance.
The Normal Distribution
GEM2900 - Understanding Unc

5.1
Five
Looking at real data
In God we trust; all others must bring data.
W. Edwards Deming
I NTRODUCTION
We often observe data that have been generated by some random process from a larger population (may be hypothetical) of measurements.
For example,

What is randomness?
As I have said so many times, God doesnt play dice with the
world.
Albert Einstein
D OES RANDOMNESS EXIST ?
For a long time, science was dominated by deterministic thinking.
The things that science dealt were either the measurements m

What is randomness?
As I have said so many times, God doesnt play dice with
the world.
Albert Einstein
1
D OES RANDOMNESS EXIST ?
For a long time, science was dominated by deterministic thinking.
The things that science dealt were either the measurements

N ATIONAL U NIVERSITY OF S INGAPORE
D EPARTMENT OF S TATISTICS AND A PPLIED P ROBABILITY
GEM2900
U NDERSTANDING U NCERTAINTY AND S TATISTICAL T HINKING
S EMESTER I, AY 2013/2014
What You Should Know About The Examinations
The Final Examination
The nal ex

N ATIONAL U NIVERSITY OF S INGAPORE
D EPARTMENT OF S TATISTICS & A PPLIED P ROBABILITY
GEM2900
U NDERSTANDING U NCERTAINTY AND S TATISTICAL T HINKING
S EMESTER I, AY 2013/2014
Supplementary Notes 3: CA 1 Exercise 6
In Exercise 6 of CA 1, I have asked you

N ATIONAL U NIVERSITY OF S INGAPORE
D EPARTMENT OF S TATISTICS & A PPLIED P ROBABILITY
GEM2900
U NDERSTANDING U NCERTAINTY AND S TATISTICAL T HINKING
S EMESTER I, AY 2013/2014
Supplementary Notes 2: Histograms and Boxplots
Shapes of Histograms
Histogram a

N ATIONAL U NIVERSITY OF S INGAPORE
D EPARTMENT OF S TATISTICS & A PPLIED P ROBABILITY
GEM2900
U NDERSTANDING U NCERTAINTY AND S TATISTICAL T HINKING
S EMESTER I, AY 2013/2014
Supplementary Notes 1: Weeks 1 and 2
Odds & Betting
Odds offered by the bookmak

GEM2900: A NSWERS TO S AMPLE PAPER A
Question 1
1
3
1
(b)
3
1
(c)
3
1
(d)
2
(a)
Question 2
(a) (i) P(A B) P(B) =
1
3
(ii) P(A B) = P(A) + P(B) P(A B) P(A) + P(B) 1 =
(iii) If A B = B in (i), A B = S in (ii)
1
6
5! 6
(b)
4
5
Question 3
(a) 0.95
(b) 0.79
(

NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION
GEM2900
Understanding Uncertainty & Statistical Thinking
(Semester N: AY YYYYYYYY)
MMM/MMM YYYY Time allowed: H hours
SAMPLE PAPER
Answer key will be released during the reading week.
INSTRUCTIONS TO CANDIDATES

NATIONAL UNIVERSITY OF SINGAPORE
EXAMINATION
GEM2900
Understanding Uncertainty & Statistical Thinking
(Semester N: AY YYYYYYYY)
MMM/MMM YYYY Time allowed: H hours
SAMPLE PAPER
Answer key will be released during the reading week.
INSTRUCTIONS TO CANDIDATES

GEM2900, 2013/2014 Semester I
Exercise Sheet 03
Suggested Solutions
1.
(i) If the bus arrives on time every day next week, his guess would be correct. Therefore,
the chance for him to be correct would be 0.65 0.078.
(ii) Carson has decided to generate the

GEM2900, 2013/2014 Semester I
Exercise Sheet 03
Exercise 1. Carson usually catches a bus scheduled to arrive at the bus stop at 7am to go
to work. However, the bus was late this morning! Carson met some friends while they were
waiting for the bus and star

GEM2900, 2013/2014 Semester I
Exercise Sheet 02
Suggested Solutions
1. We use the letters A, B and C for the events component A works, component B works,
and component C works respectively. Now the apparatus will work if either A and B
are working, or C i

GEM2900, 2013/2014 Semester I
Exercise Sheet 02
Exercise 1. The electrical apparatus in the diagram below works so long as current can ow
from left to right. The three components are independent.
The probability that component A works is 0.8; the probabil

GEM2900, 2013/2014 Semester I
Exercise Sheet 01
Exercise 1. Refer to Example 1.7 in the lecture notes. With odds oered for both games, you
choose to place a stake of $5 on the 1st game and a stake of $5 on the 2nd game. What will
happen?
Exercise 2. Refer

6.1
Six
I NTRODUCTION
In many situations when a random experiment is performed, we are
interested in some function of the outcome rather than the outcome
itself.
Random Variables
Two random variables were gossiping and thought they
were discrete by whispe

N ATIONAL U NIVERSITY OF S INGAPORE
D EPARTMENT OF S TATISTICS & A PPLIED P ROBABILITY
GEM2900
U NDERSTANDING U NCERTAINTY AND S TATISTICAL T HINKING
S EMESTER I, AY 2013/2014
e-learning week information
As scheduled by the University, Week 5 (9 to 13 Sep

Two
The Rule Book
But to us, probability is the very guide of life.
Bishop Joseph Butler
2.1
I NTRODUCTION
In the previous chapter, we learnt about the various interpretations of probability. Whatever approach you use, consistency is required.
In this cha

Review
1
C HAPTER 1
Chance experiment: a process with uncertainty about resulted
outcomes.
Event: collection of possible outcomes from a chance experiment.
Interpretations of Probabilities:
Propensities (classical);
Long-run relative frequency;
Degr

Four
Probability via Counting
. . . the White Queen asked. Whats one and one and one
and one and one and one and one and one and one and one?"
I dont know," said Alice. I lost count."
Lewis Carroll
108
4.1
I NTRODUCTION
Obviously, P(A) can only be dened i

Two
The Rule Book
But to us, probability is the very guide of life.
Bishop Joseph Butler
33
2.1
I NTRODUCTION
2.2
In the previous chapter, we learnt about the various interpretations of
probability. Whatever approach you use, consistency is required.
In t

GEM2900
Understanding Uncertainty and Statistical Thinking
Academic Year 2013/2014
Semester I
A IMS & O BJECTIVES
Course Information
iii
This module, using a minimum of mathematical or statistical prerequisites, aims to help the student make rational deci

GEM2900
Understanding Uncertainty
and Statistical Thinking
Academic Year 2013/2014
Semester I
David Chew
Department of Statistics and Applied Probability
email: david.chew@nus.edu.sg
Typesetted using the MiKTEX sytem.
Course Information
A IMS & O BJECTIVE

GEM2900, 2013/2014 Semester I
Continuous Assessment 03
Instructions
This is the last of a series of continuous assessments for this module.
Each correct answer to a question is worth two (2) marks.
This question sheet is available from the module workbin

GEM2900, 2013/2014 Semester I
Continuous Assessment 02
Suggested Solutions
1. The answer is (b).
The probability that you choose correctly initially is 1/3 and this doesnt change if you
stick with your initial choice no matter what.
2. The answer is (b).

GEM2900, 2013/2014 Semester I
Continuous Assessment 02
Instructions
This is the second of a series of continuous assessments for this module.
Each correct answer to a question is worth two (2) marks.
This question sheet is available from the module workbi

GEM2900, 2013/2014 Semester I
Continuous Assessment 01
Instructions
This is the rst of a series of continuous assessments for this module.
Each correct answer to a question is worth two (2) marks.
This question sheet is available from the module workbin f