NTHU MATH 2820, 2008, Lecture Notes
Ch1~6, p.1
Chapter 1
Question
There are many random phenomena (
example?
) in our real
life. What is the language/mathematical structure that we use to
depict them?
Outline
¾
sample space
¾
event
¾
probability measure
• conditional probability
• independence
¾
three theorems
• Multiplication Law
• law of total probability
• Bayes’ rule
made by ShaoWei Cheng (NTHU, Taiwan)
Ch1~6, p.2
Definition
(sample space, TBp. 2)
Question
What are the differences between the
Ω
in these examples?
Example 1.1
(throw a coin 3 times, TBp. 35)
Example 1.2
(number of jobs in a print queue, Ex. B, TBp. 2)
Example 1.3
(length of time between successive earthquakes, Ex. C, TBp. 2)
A
sample space
Ω
is the set of all possible outcomes in a
random phenomenon.
Ω
=
{
hhh, hht, hth, thh, htt, tht, tth,ttt
}
Ω
=
{
0
,
1
,
2
,...
}
Ω
=
{
t

t
≥
0
}
Ω
is a finit set
Ω
is an infinite, but countable, set
Ω
is an infinite, but uncountable, set