# 4 that n n 1 1 e x e xk e x e x n n k1 k1 and 2 x n n

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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.

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