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Unformatted text preview: Lecture 17 17.1 Confidence intervals for parameters of nor mal distribution. We know by LLN that sample mean and sample variance converge to mean and variance 2 : X , X 2 ( X ) 2 2 . In other words, these estimates are consistent. In this lecture we will try to describe precisely, in some sense, how close sample mean and sample variance are to these unknown parameters that they estimate. Let us start by giving a definition of a confidence interval in our usual setting when we observe a sample X 1 , . . . , X n with distribution from a parametric family { : } , and is unkown. Definition: Given a parameter [0 , 1] , which we will call confidence level, if there are two statistics S 1 = S 1 ( X 1 , . . . , X n ) and S 2 = S 2 ( X 1 , . . . , X n ) such that the probability ( S 1 S 2 ) = , ( or ) then we call the interval [ S 1 , S 2 ] a confidence interval for the unknown parameter with the confidence level ....
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This note was uploaded on 10/11/2009 for the course STATISTICS 18.443 taught by Professor Dmitrypanchenko during the Spring '09 term at MIT.
 Spring '09
 DmitryPanchenko
 Statistics, Normal Distribution, Variance

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