I am a student studying statistics and I have some questions about $E(X)$.

Am I right in understanding that $E[X+Y]=E[X]+E[Y]$ for every random variable $X$ and $Y$, but $V[X+Y]=V[X]+V[Y]$ only when $X$ and $Y$ are independent?

Thank you for your time!

+) I noticed that the comments below refer to independence and uncorrelation as different concepts, but I'm not exactly sure how:( Could someone please elaborate??