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Unformatted text preview: ]. • the 95% conﬁdence level means that for 95% of the samples, µ is in the CI
computed according to (4.2)
This can be seen from the derivation of (4.2).
More examples. See Examples 4.2.1 and 4.2.2 in the book.
4.1.2 More about X
Let Xk be independent observations from the same distribution; in other words, a random
2
2
sample. We denote the distribution by X . Then, for each k , E (Xk ) = E (X ) and σXk = σX .
n 1
Since X = k=1 n Xk , it follows using the formulas at the end of §2.6.4 that
n
n
1
1
E (X ) =
E (Xk ) =
E (X ) = E (X )
n
n
k=1
k=1 and
2
σX n
n
1
1
12
2
=
σ=
σ 2 = σX ,
2 Xk
2X
n
n
n
k=1
k=1 hence 1
σX = √ σX
n Thus X is an unbiased estimator of µX , and its standard deviation is decreasing with the...
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This note was uploaded on 02/05/2014 for the course MATH 3339 taught by Professor Staff during the Fall '08 term at University of Houston.
 Fall '08
 Staff
 Statistics

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