lecture07 notes

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Unformatted text preview: Stat 312: Lecture 06 Quantile-quantile plots Moo K. Chung mchung@stat.wisc.edu September 23, 2004 1. In order to compute 100(1- )% confidence interval, it is required to find z / 2 that satisfies P ( Z > z / 2 ) = / 2 for given . We will study how to find z / 2 and more. This lecture is based on Chapter 4.6. 2. The p-th quantile point q for random variable X is the point such that F ( q ) = P ( X q ) = p. The textbook represent it in terms of percentile . Note that p-th quantile = 100 p-th percentile. So given p , q = F- 1 ( p ) . For X N (0 , 1) , it is easy to find the p-th qun- tile using > qnorm(1) [1] Inf > qnorm(0.5) [1] 0 > qnorm(0) [1] -Inf > qnorm(0.5) [1] 0 > qnorm(0.95) [1] 1.644854 > qnorm(0.05) [1] -1.644854 In order to find z , we use command qnorm ( 1- ) . 3. Given n observations x 1 , ,x n , we order them from the smallest to the largest and we have x (1) , ,x ( n ) . The i-th smallest observation is defined as the ( i- . 5) /n...
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This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Fall '04 term at Wisconsin.

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lecture07 notes - Stat 312: Lecture 06 Quantile-quantile...

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