How to determine the expectation $\mathbb{E}(cXY)$ I am looking for a formula to determine the expectation $\mathbb{E}(cXY)$
I have earlier determined the $\mathbb{E}(XY)$, since this was more easy to determine. However, instead of the variable $X$ I need to consider $cX$. Is it correct that therefore the new expectation also becomes $\mathbb{E}(cXY)$ and does anyone know how to determine this expectation? My intuition says that you can take the constant out of the expectation and therefore get $c\mathbb{E}(XY)$, but I cannot find this anywhere explicitly. X and Y are not independent.

Define $Z = XY$, assuming that by $c$ you mean a constant, then by the linearity of expectation $E[cZ] = cE[Z]$, so you are correct.
