**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 X-E 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 X-E X equals-5 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 2-2 E ( XM ) + E ( M 2 ) = E X 2-2 M 2 + M 2 = E X 2-( E X ) 2 . 1...

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- Fall '06
- SCHWAGER
- Variance, Probability theory, var, 2m, yp