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Unformatted text preview: normal distribution N( , 2 ), then distribution of the sample mean X is Ping Ma Lecture 20 Fall 2005 2 Theorem 6.32 Let the distribution of independent random variables X1, X2, , Xn be 2 (r1), 2 (r2),, 2 (rn), respectively, then distribution of Y= X1+X2+ +Xn is 2 (r1+r2++rn) Theorem 6.33 If Z1, Z2, , Zn are observations of a random sample of size n from a standard normal distribution N(0,1), , then W= Z1 2 +Z2 2 + +Zn 2 ~ 2 (n) Ping Ma Lecture 20 Fall 2005 3 If X1, X2, , Xn are observations of a random sample of size n from a normal distribution N( , 2 ), then we have (a) X and S 2 are independent (b) 2 2 ) 1 ( S nis 2 (n1) Ping Ma Lecture 20 Fall 2005 4 ...
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 Fall '05
 TBA
 Statistics, Variance

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