GEM2900 - Understanding Uncertainty & Statistical Thinking
Semester 1, 2012/2013
NUS/FOS/DSAP
Lecture 3 – 1
GEM 2900
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&
Understanding Uncertainty &
Statistical Thinking
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3
Lecture 3

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GEM2900 - Understanding Uncertainty & Statistical Thinking
Semester 1, 2012/2013
NUS/FOS/DSAP
Lecture 3 – 2
Sample Space & Events
Chance Experiment
A process with uncertainty about
resulted outcomes
Sample Space
Collection of all possible outcomes of a
chance experiment. Usually denoted by
S
Event
Any collection of outcomes from the sample
space.
◊
An event is a subset of the sample space,
S
.
◊
Typically, we are interested in some specific
events.

GEM2900 - Understanding Uncertainty & Statistical Thinking
Semester 1, 2012/2013
NUS/FOS/DSAP
Lecture 3 – 3
Sample Space & Events
Example
...
(a)
Chance experiment:
Toss a coin twice
Sample space:
S
=
{HH, HT, TH, TT}
... the sample space is discrete (countable)
Event A
=
{HH}
Event B
=
{HT, TH}
(b)
Chance experiment:
Waiting time till
the next bus arrives
l
Sample space:
S
=
{
x: x
> 0
}
=
[
0,
∞
)
... the sample space is continuous (interval)
E
t A {
0
≤
≤
2
} [
0 2
]
Event A
=
{
x:
0
x
}
=
[
0, 2

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