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Math Help - the variance of the sum of XiUi if the variance of ui depends on Xi

  1. #1
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    the variance of the sum of XiUi if the variance of ui depends on Xi

    I am told that the variance of Ui given x is sigma squared times Xi and that the covariances between all ui is equal to sigma squared

    if I want the variance of \sumx_iu_i and I break it down so i have the variance of  \sumx_1u_1 + \sumx_i_i (from i=2 to n) I will end up having to compute var(x_1u_1)

    Can I take x out of the summation if the variance of u is dependent on x?

    ie can I do this var(x_1u_1) = x^2Var(u1)
    Last edited by kingsolomonsgrave; October 3rd 2013 at 05:07 PM.
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  2. #2
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    Re: the variance of the sum of XiUi if the variance of ui depends on Xi

    Hey kingsolomonsgrave.

    You won't be able to do that in general. Are these distributions joint Normal? If so do they have a covariance structure?

    Remember that you stated Var[Ui|Xi=x] = sigma^2*Xi which is not in general equal to Var[Ui*Xi].
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