Chapter 4.4, Problem 12E

Show that in the bivariate situation, E is a linear or distributive operator. That is, show that

$E\left[a_1{u}_1\left(X,Y\right)+a_2{u}_2\left(X,Y\right)\right]+a_{1}E\left[u_1\left(X,Y\right)\right]+a_{2}E\left[u_2\left(X,Y\right)\right]$