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!