Show that if $X$ and $Y$ are independent rv's, then $E(XY)=E(X)\cdot E(Y)$. Then apply this in Exercise 25(Here is Question2504). [{\it Hint:} Consider the continuous case with $f(x,y)=f_X(x)\cdot f_Y(y)$.]
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By definition, $X$ and $Y$ are independent if the joint pmf or pdf is equal to the product of the marginal pmf's or pdf's. That is, $f(x,y)=f_X(x)\cdot f_Y(y)$.
We consider the continous case
\[
\begin{split}
E(XY)&=\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}xy\cdot f(x,y)dxdy\\
&=\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}xy\cdot f_X(x)f_Y(y)dxdy\\
&=\int_{-\infty}^{+\infty}xf_X(x)dx\cdot\int_{-\infty}^{+\infty}yf_Y(y)dy\\
&=E(X)\cdot E(Y)
\end{split}
\]