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WEEK 1 – Sept 1
Go over
Syllabus
.
Go over
Tentative Schedule
.
Expected Coverage for Today
.
Ideas in Chapter 2, Sections 21 through 24.
Types of probability
:
objective
and
subjective
Probability models
are used to mathematically model situations where outcomes are
uncertain.
Models can be useful although they cannot be proved to be correct.
Example 1.
A Coin Toss.
I flip an ordinary coin, say, a U.S. quarter and let it land on a
flat surface.
Consider a model that ignores the possibility that it comes to rest on its edge.
Then there are two possible outcomes for the upper face: Heads (H) and Tails (T).
When
we say the coin is
fair
, we imply that the two outcomes are equally likely.
A mathematical
expression for this is P(H) = P(T) = ½.
The
sample space
S
in the model is the collection
of possible
outcomes
{H, T}.
Here is a figure to display this probability model.
½
½
. H
.T
S
We might even use the simpler figure without the probabilities shown and simply state that
the two outcomes are equally likely.
. H
.T
S
1
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View Full DocumentExample 2.
Figure showing sample space with 11 outcomes.
If the model specifies
them as equally likely, then we know each has probability 1/11.
The names of outcomes
not shown in figure below; they are simply depicted by dots.
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S
Example 3.
Model for independent tosses of three fair coins
(say a nickel, a dime and a
quarter).
In the table below, the first letter denotes the outcome of the nickel, the second
letter denotes the outcome of the dime, and the third letter denotes the outcome of the
quarter.
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 Fall '09
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