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Confidence
Intervals
Section 8.1
Lecture 29
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View Full Document Confidence Intervals
•
The Central Limit Theorem tells us that the
average of a large number of independent,
identically distributed random variables is
approximately normally distributed:
2
1
1
~,
n
i
i
X
X
N
nn
Example
•
Let X be the outcome of the roll of a fair six
sided die.
Then
E
(
X
) = 3.5 and
Var
(
X
) =
2.917.
If we roll the die many times, then we
would expect the average outcome to be close
to
μ
= 3.5.
But how close?
And how certain
can we be?
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View Full Document Definition
•
The number
μ
is an attribute of the dice.
It
may be unknown in practice.
A fair die has
μ
= 3.5 but you may not be sure that the die is
fair.
μ
is called a
parameter
of the distribution
of
X
.
•
The value
depends on the experiment.
If
another person rolls the die many times, he
may obtain a slightly different
.
This number
is called a
statistic
.
What allows us to do
computations is that we know the
distribution
of the statistic.
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This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University.
 Spring '08
 MARTIN
 Central Limit Theorem

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