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Math Help - Linear Combinations of Variance

  1. #1
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    Linear Combinations of Variance

    Is this true?

     Var(5X_1-3X_2) = 5^2Var(X_1)+(-3)^2Var(X_2)

    or is it

     Var(5X_1-3X_2) = 5^2Var(X_1)-(3)^2Var(X_2)
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  2. #2
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    im afraid its neither unless X1 and X2 are uncorrellated.


    if they are uncorrelated, it would be the first one....i think
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  3. #3
    MHF Contributor matheagle's Avatar
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     Var(5X_1-3X_2) = 5^2Var(X_1)+(-3)^2Var(X_2)+2(5)(-3)Cov(X_1,X_2)
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