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Math Help - covariance problem

  1. #1
    ixi
    ixi is offline
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    covariance problem

    Let X1, X2, and X3 be uncorrelated random variables, each with mean u and variance sigma^2. Find, in means of u and sigma^2, Cov(X1+X2, X2+X3)

    I got this far:

    Cov(X1+X2, X2+X3) = E[(X1+X2)(X2+X3)] - E(X1+X2)E(X2+X3)

    But i don't know how to continue this problem

    thanks
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  2. #2
    MHF Contributor

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    Quote Originally Posted by ixi View Post
    Let X1, X2, and X3 be uncorrelated random variables, each with mean u and variance sigma^2. Find, in means of u and sigma^2, Cov(X1+X2, X2+X3)

    I got this far:

    Cov(X1+X2, X2+X3) = E[(X1+X2)(X2+X3)] - E(X1+X2)E(X2+X3)

    But i don't know how to continue this problem

    thanks
    Now expand, use linearity of the expectation, and the assumptions...
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  3. #3
    MHF Contributor matheagle's Avatar
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    I just obtain the 4 covariances...

    Cov(X_1+X_2, X_2+X_3)= Cov(X_1,X_2)+Cov(X_1,X_3)+Cov(X_2,X_2)+Cov(X_2,X_3  )

    = 0+0+V(X_2)+0=\sigma^2

    It's just like (a+b)(c+d)=ac+ad+bc+bd
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