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

• Oct 3rd 2013, 04:54 PM
kingsolomonsgrave
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 \$\displaystyle \sumx_iu_i\$ and I break it down so i have the variance of \$\displaystyle \sumx_1u_1 + \sumx_i_i\$ (from i=2 to n) I will end up having to compute \$\displaystyle 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 \$\displaystyle var(x_1u_1) = x^2Var(u1)\$
• Oct 4th 2013, 05:09 AM
chiro
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].