NotesSep20 - 3 Corollary from Properties 1 and 2 For any...

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Unformatted text preview: 3 . ( Corollary from Properties 1 and 2 ) For any random variables X and Y , and num- bers a,b E ( aX + bY ) = aEX + bEY. This is the general linearity property of the ex- pectation. This property extends to more than 2 random variables: for any random variables X 1 ,...,X n , E ( X 1 + ... + X n ) = EX 1 + ... + EX n . More generally: for any random variables X 1 ,...,X n and numbers a 1 ,...,a n , E n X i =1 a i X i = n X i =1 a i EX i . 4 . A degenerate random variable If a random variable is a constant: X = b , then its mean is equal to the same constant: EX = b . 5 . If X and Y are independent random vari- ables then E ( XY ) = E ( X ) E ( Y ) . Variance and standard deviation Let X be a random variable with mean EX = μ . Recall that the variance of X is defined as Var( X ) = E h ( X- μ ) 2 i . Sometimes the notation Var X will be used. Some use the notation V ( X )....
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This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell.

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NotesSep20 - 3 Corollary from Properties 1 and 2 For any...

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