I am not sure how to determine the variance and mean for the following equation system. I'd greatly appreciate your help!
$ f_\xi(x) = \left\{ \begin{array}{l l} 10k_1x & \quad \text{for $0
$ f_\eta(x) = \left\{ \begin{array}{l l} 4k_2x & \quad \text{for $0
I have determined the following:
$k_1 = \frac{1}{5}$
$k_2=\frac{2}{7}$
... and I believe to have found their individual variance and mean:
$E_\xi(x)=\frac{2}{3}$
$V_\xi(x)=\frac{1}{18}$
$E_\eta(x)=\frac{22}{21}$
$V_\eta(x)=\frac{145}{882}$
Now to the gist of my question: how do I calculate the variance and the mean for $10\xi+2\eta$? Thank you!