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1
STAT 5112
Spring 2012
Lecture 5
Jan 20, 2012
Jun Xie
2 Introduction of Probability
Probability is a chance measurement defined on sample space and for events of a random experiment.
An experiment
is any activity or process whose outcome is subject to uncertainty.
The sample space
of an experiment, denoted by
S
, is the set of all possible outcomes of that experiment.
Example
Experiment of tossing a coin,
S
={Head, Tail}
Experiment of tossing a die,
S
={1,2,3,4,5,6}
An event
is any collection (subset) of outcomes contained in the sample space.
An event is simple if it consists of exactly one outcome and compound if it consists of more than one
outcome.
Event = Set
Operations
1.
Complement A’=
S
\A
2.
Union,
? ∪ ?
, “A or B”
3.
Intersection,
? ∩ ?
, “A and B”
Example 8
Let
S
={0,1,2,3,4,5,6}, A={0,1,2,3,4}, B={3,4,5,6}, C={1,3,5}. Then
A’={5,6}
? ∪ ?
={0,1,2,3,4,5,6}=
S
? ∪ ?
={0,1,2,3,4,5}
? ∩ ?
={3,4}
? ∩ ?
={1,3}
(
? ∩ ?
)
′
={0,2,4,5,6}
Null event
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 Fall '08
 BUD
 Probability

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