Unformatted text preview: X . The variance measures how much spread there is about the expected value. Example. We toss a fair coin and let X = 1 if we get heads, X =1 if we get tails. Then E X = 0, so XE X = X , and then Var X = E X 2 = (1) 2 1 2 + (1) 2 1 2 = 1. Example. We roll a die and let X be the value that shows. We have previously calculated E X = 7 2 . So XE X equals5 2 ,3 2 ,1 2 , 1 2 , 3 2 , 5 2 , each with probability 1 6 . So Var X = (5 2 ) 2 1 6 + (3 2 ) 2 1 6 + (1 2 ) 2 1 6 + ( 1 2 ) 2 1 6 + ( 3 2 ) 2 1 6 + ( 5 2 ) 2 1 6 = 35 12 . Note that the expectation of a constant is just the constant. An alternate expression for the variance is Var X = E X 22 E ( XM ) + E ( M 2 ) = E X 22 M 2 + M 2 = E X 2( E X ) 2 . 1...
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 Fall '06
 SCHWAGER
 Variance, Probability theory, var, 2m, yp

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