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1
Section 2.1
•
Set Theory
:
•
Containment
(
subset
)
•
Equality
identical
)
•
Union
combination
)
A U B
•
Intersection
commonality
)
A
∩
B
•
Complementation
negation / not in
)
A
c
•
De Morgan’s Laws
:
•
•
• Sample spaces and events
•
Experiments
– a process whose outcome is unknown (
eg: roll a die
)
•
Sample spaces
– set of all possible outcomes of an experiment
(
eg: S = {1,2,3,4,5,6})
•
Events
– a subset of the sample space (
eg: E={2,4,6}
)
Recap ….
AB
∩
A
= B
iffAB
&
Today ….
Axioms and Properties of Probability
Axiom:
A1) P(
S
) = 1
A2) P(
E
)
≥
0
for every event
E
S
A3) For mutually exclusive events,
Properties:
1) P(
) = 0
2)
3)
4)
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What is Probability?
What do we mean when we say the probability of an event is something?
(Long Term Frequency) Frequentist Interpretation of Probability
The probability of an event
E
is the long term proportion of the time
that the experimental outcome is
E
, when the experiment is
repeated
many times
under the
identical experimental conditions
:
m
n
= # of times
E
occurs in
n
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This document was uploaded on 07/26/2011.
 Spring '09
 Statistics

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