Let $x_1,x_2,$dots,$x_k$ be continuous random variables with joint distribution $f(x_1,x_2,$dots,$x_k).$ For each $i=1,2,$dots,$k,$ let $g_i$:$D_{i}R$ be a function whose domain contains the range of $x_i.$ Let $a,a_1,$dots,$a_{k}inR.$ Show that, $E(a+{\displaystyle \underset{i=1}{\overset{k}{}}}{a}_i{g}_i(x_i))=a+{\displaystyle \underset{i=1}{\overset{k}{}}}{a}_{i}E(g_i(x_i))$ or written out, $E(a+a_1{g}_1(x_1)+$dots$+a_k{g}_k(x_k))=a+a_{1}E(g_1(x_1))+$dots$+a_{k}E(g_k(x_k))$