elemprob-fall2010-page25

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As an example, let g ( x,y ) = x + y . Then E ( X + Y ) = X x,y ( x + y ) P ( X = x,Y = y ) = X x X y x P ( X = x,Y = y ) + X y X x y P ( X = x,Y = y ) = X x x P ( X = x ) + X y y P ( Y = y ) = E X + E Y, a result we had previously proved another way.
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