Lecture 12-2008 - Normal Random Variables Lecture XII I....

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Normal Random Variables Lecture XII I. Univariate Normal Distribution. A. Definition 5.2.1. The normal density is given by     2 2 11 exp , 0 2 2 x f x x            When X has the above density, we write symbolically   2 ~, XN  . B. Theorem 5.2.1. Let X be   2 , N . The   EX  and   2 VX  .     2 2 2 exp 2 2 x E X x dx    1. Using the change in variables technique, we create a new random variable z such that x z x z dx dz  Substituting into the original integral yields:     2 22 2 exp 2 2 exp 2 2 exp 2 2 E X z z dz z z dz z dz      Taking the integral of the first term first, we have: 2 2 2 2 1 1 1 exp exp 2 1 exp 0 2 z z dz C z z dz Cz     
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AEB 6933 Mathematical Statistics for Food and Resource Economics Lecture XII Professor Charles B. Moss Fall 2007 2 2. The value of the second integral becomes
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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Lecture 12-2008 - Normal Random Variables Lecture XII I....

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