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Chapter 2, Sections 45
A Probability Model
The Discrete Case
©
John J Currano, 01/25/2010
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Terminology
±
(Random) Experiment
• The outcome cannot be predicted with certainty
• The set of all possible outcomes can be described
±
Examples
• Toss a coin and observe the face that shows
• Toss a die and observe the top face
• Sample output from an industrial process
±
Sample Space
– Set of all possible outcomes
• Its elements are called
Sample Points
or
Outcomes
• Its subsets are called
Events
•
Simple Event
: a subset with only one outcome
•
Compound Event
: subset with more than one outcome
3
Terminology
±
(Random) Experiment
±
Sample Space
– Set of all possible outcomes
• Subsets:
Events
• Elements:
Sample Points
or
Outcomes
±
Discrete Sample Space
– Finite or Countably Infinite
Example
: Toss a die and observe the top face
S
1
= { 1, 2, 3, 4, 5, 6 }
S
2
= { even, odd }
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Terminology
±
(Random) Experiment
±
Sample Space
– Set of all possible outcomes
±
A
Probability Model
for an experiment consists of:
•A
Sample Space
,
S
Probability Measure
on
S
A realvalued function,
P
, defined on the subsets
of
S
(the events) that satisfies certain axioms
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5
Axiom 3 is known as
countable additivity
and states that the
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This note was uploaded on 02/23/2011 for the course MATH 444 taught by Professor Any during the Fall '10 term at Roosevelt.
 Fall '10
 Any
 Statistics, Probability

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