Expected value of functions of random variables Is the following correct 
$$ \mathbb{P}[ X >(Y+Z)] = E_{Y}\left(\mathbb{P}[ X >(y+Z)]_{y=Y}\right)$$ 

\begin{align}
 \mathbb{P}\left( X >(Y+Z)\right) &= \int_{}f_y(y)\mathbb{P}\left( X >(y+Z)\right) \\&= E_{Y}\left(\mathbb{P}[ X >(y+Z)]\right)
\end{align}
