Are the following two statements correct?
$\mathbb{E}[X\mathbb{E}(Y)] = \mathbb{E}(X)\mathbb{E}(Y),$ and
$\mathbb{E}[X(aY-a\mathbb{E}(Y))] = a\mathbb{E}[XY]-a\mathbb{E}[X]\mathbb{E}[Y] = a Cov(X,Y)$,
where $X$ and $Y$ are some (possibly dependent) random variables and $Cov(X,Y)$ stands for the covariance of $X$ and $Y$.
Thanks a lot for your help!