This preview shows page 1. Sign up to view the full content.
Unformatted text preview: the observations we made last time: the expected value and variance of X are as we have already seen they must be. But even more: the sample mean is itself normal, so these two numbers tell the whole story. We restate this important result: Fact. If X 1 , . . ., X n are iid n ( , 2 ), then X is n ( , 2 /n ). (5.3.1.b) Next, we turn to the distribution of the sample variance S 2 when samples of size n are drawn from an n ( , 2 ) distribution. Fact. X and S 2 are independent. (5.3.1.a) Fact. ( n1) S 2 / 2 has a 2 n1 (chi squared with n1 degrees of freedom) distribution. (5.3.1.c)...
View
Full
Document
This note was uploaded on 11/29/2011 for the course MATH 4056 taught by Professor Staff during the Fall '08 term at LSU.
 Fall '08
 Staff
 Statistics, Normal Distribution

Click to edit the document details