Unformatted text preview: Var X = E X 2( E X ) 2 = ( ba ) 2 12 . 12 Normal distribution A random variable is a standard normal (written N (0 , 1)) if it has density 1 √ 2 π ex 2 / 2 . A synonym for normal is Gaussian. The ﬁrst thing to do is show that this is a density. Let I = R ∞ ex 2 / 2 dx. Then I 2 = Z ∞ Z ∞∞ ex 2 / 2 ey 2 / 2 dxdy. 28...
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This note was uploaded on 12/29/2011 for the course MATH 316 taught by Professor Ansan during the Spring '10 term at SUNY Stony Brook.
 Spring '10
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