Let $X, Y, Z$ be independent standard normal variables. What is $\mathbb{E}(X+Y-Z)^2$?
n.b.: this is review, not homework. I just wanted to double-check my own answer.
Let $Q:=X+Y-Z$. $$\mathbb{E}Q^2 = 3\mathbb{E}(\frac{Q}{\sqrt{3}})^2=3$$
Since $(\frac{Q}{\sqrt{3}})^2$ follows a chi-squared distribution with 1 d.f., i.e. its mean is $1$.