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Unformatted text preview: Stochastic Signals and Systems Multiple Random Variables Virginia Tech Fall 2008 Expected Value of Functions of RVs The problem of finding the expected value of a function of 2 or more random variables is similar to that of finding the expected value of a function of a single random variable. It can be shown that the expected value of Z = g ( X , Y ) can be found using the following expressions: E [ Z ] = Z ∞-∞ zf Z ( z ) dz = Z ∞-∞ Z ∞-∞ g ( x , y ) f X , Y ( x , y ) dxdy if X , Y are jointly continuous, and E [ Z ] = X i X n g ( x i , y n ) p X , Y ( x i , y n ) if X , Y are discrete. Expected Value of a Sum of n RVs Let Z = X 1 + X 2 + ... + X n . Find E [ Z ] . The expected value of a sum of n random variables is equal to the sum of the expected values E [ X 1 + X 2 + ... + X n ] = E [ X 1 ] + E [ X 2 ] + ... + E [ X n ] Note that the random variables do not have to be independent !...
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- Fall '08