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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.

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