What's $\mathbb{E}(|X-Y|)$ or $\mathbb{E}(X / (Y+1))$?
For $\mathbb{E}(|X-Y|)$ I think I could simply list all the possible values of $|X-Y|$ and then (assuming they all have the same probability) just calculate
$\mathbb{E}(|X-Y|)=P_{|X-Y|} \cdot (sum + of + all + possible + values + of + |X-Y|)$
But what about the second one? I think I could (assuming $X,Y$ id) split
$\mathbb{E}(X / (Y+1))=\mathbb{E}(X)\mathbb{E}(\frac{1}{Y+1})$,
but what's $\mathbb{E}(\frac{1}{Y+1})$?
I assume you work in a discrete setting. The definition for $\mathbb{E}(X)$ is:
$$ \mathbb{E}(X) = \sum{x \cdot \mathbb{P}(X=x)} $$
In your case:
$$ \mathbb{E}(\dfrac{X}{Y+1}) = \sum{\dfrac{x}{y+1} \cdot \mathbb{P}(X=x, Y=y)} $$
Assuming $X$ and $Y$ are independent means: $\mathbb{P}(X=x, Y=y) = \mathbb{P}(X=x)\cdot\mathbb{P}(Y=y)$