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Unformatted text preview: ependent normal variables is normal — is not proven in this book.
1 2 In particular, we see that E (X ) = µ.
Note. It is always true that X , the sample mean, is an unbiased estimator 4 of µ, the
population mean. See §4.1.2 below.
CI. Compute the CI
From Ds, we know how X behaves. We draw a sample, and we compute the statistics for
it. In our case, we obtain a value x (see top of page 218 again for estimator, X , vs. estimate,
x). We are now asking: what are the likely values of µ, given that we observed x?
Since5
σ2
X −µ
X ∼ N µ,
⇐⇒
∼ N (0, 1))
σ
√
n
n
we conclude that
X − µ
P σ ≤ zα/2 = P [Z  ≤ zα/2 ] = 1 − α
√n (4.1) where (see Table C.4, bottom right part; zα is called an...
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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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