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Recap ….
• The study of
randomness
and
uncertainty
• “Chances”, “odds”, “likelihood”, “expected”, “probably”, “on average”, .
..
Probability
(section 1.1)
Population
Sample
PROBABILITY
INFERENTIAL
STATISTICS
Section 2.1
Today ….
•
Set (Theory) Algebra
•
Just some “Shorthand notations” for long sentences
•
Why do we need this shorthand
•
Probability measures are assigned to subsets of a set
•
Operations on sets
•
containment, equality, union, intersection, complementation
•
DeMorgan’s Law
•
Formulation
•
Sample spaces and events

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Sample Spaces
Outcome:
a possible result of the random phenomenon studied.
Experiment:
any process leading to an uncertain outcome.
(but it is known that the outcome will be one of several possible outcomes).
The
sample space
of an experiment is the set of
all
possible outcomes.
Example: Toss a coin:
Observe Temperature
at 7AM at Columbus airport.
S?
Roll a six-sided die:
Section 2.1
We will denote the sample space by
S
.
S = { heads, tails }
= { H, T }
S = { 1,2,3,4,5,6 }
Eamples of Sample Spaces
Section 2.1

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